Method and system for analyzing reactions using an information system

ABSTRACT

A method and system for determining the quantity of an analyte initially present in a chemical and or biological reaction as well as a computer implemented method and system to automate portions of the analysis comprising mathematical or graphical analysis of an amplification reaction.

RELATED APPLICATIONS

The present application claims priority from of co-pending U.S.Provisional Patent Application No. 60/527,389, filed Dec. 6, 2003.

COPYRIGHT NOTICE

Pursuant to 37 C.F.R. 1.71(e), applicants note that this disclosurecontains material that is subject to and for which is claimed copyrightprotection, such as, but not limited to, source code listings, screenshots, user interfaces, user instructions, and any other aspects of thissubmission for which copyright protection is or may be available in anyjurisdiction. The copyright owner has no objection to the facsimilereproduction by anyone of the patent document or patent disclosure, asit appears in the records of the Patent and Trademark Office. All otherrights are reserved, and all other reproduction, distribution, creationof derivative works based on the contents, public display, and publicperformance of the application or any part thereof are prohibited byapplicable copyright law.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to analysis of data of nucleic acidamplification reactions. More specifically, the invention relates to aninformation system and method for making determinations regardingchemical and/or biological reactions. The invention also involves analternate method of quantifying nucleic acids in a sample comprisingamplification of a target nucleic acid and analysis of data obtainedduring the amplification reaction. The invention further involves adiagnostic system and/or kit using real-time nucleic acid amplificationincluding, but not limited to, PCR analysis.

2. Discussion of the Art

In many different industrial, medical, biological, and/or researchfields, it is desirable to determine the quantity of a nucleic acid ofinterest. Some methods of quantifying nucleic acids of interest involveamplifying them and observing a signal proportional to the quantity ofamplified products made; other methods involve generating a signal inresponse to the presence of a target nucleic acid, which signalaccumulates over the duration of the amplification reaction. As usedherein, nucleic acid amplification reaction refers both to amplificationof a portion of the sequence of a target nucleic acid and toamplification and accumulation of a signal indicative of the presence ofa target nucleic acid, with the former often being preferred to thelatter. The quantification of nucleic acids is made more difficult orless accurate or both because data captured during amplificationreactions are often significantly obscured by signals that are notgenerated in response to the target nucleic acid (i.e., noise).Furthermore, the data captured by many monitoring methods can be subjectto variations and lack of reproducibility due to conditions that canchange during a reaction or change between different instances of areaction. In view of the above, there is a need to develop improvedmeans of quantifying a nucleic acid. Where quantification of nucleicacids is enabled by amplification reactions, there is also a need toimprove current methods of detecting suspect or invalid amplificationreactions. There further remains a need to improve current abilities todistinguish between amplification reactions that do not detect a targetnucleic acid (i.e., negative reactions) from weak signals obtained fromamplification reactions suffering from low quantities of a targetnucleic acid in a sample, a degree of inhibition of the amplificationreaction, or other causes. The present invention provides improvementsin these areas as is disclosed below.

A non-exhaustive list of references providing background informationregarding the present invention follows:

-   -   Livak, K. and Schmittgen, T., Analysis of Relative Gene        Expression Data Using Real-Time Quantitative PCR and the 22DDCT        Method, METHODS 25: 402-408 (2001) doi: 10.1006/meth.2001.1262.    -   Bustin S A, Absolute quantification of mRNA using real-time        reverse transcription PCR assays, Journal of Molecular        Endocrinology 25: 169-193 (2000).

Bustin S A., Quantification of mRNA using real-time reversetranscription PCR: trends and problems, J Mol Endocrinol. 29: 23-29(2002).

While the inventors cannot guarantee that the following website willremain available and do not necessarily endorse any opinions expressedtherein, an interested person may wish to refer to the websitewww.wzw.tum.de/gene-quantification/index.shtml for useful backgroundinformation.

The discussion of any works, publications, sales, or activity anywherein this submission, including in any documents submitted with thisapplication, is not intended to be an admission of any manner that anysuch work constitutes prior art, unless explicitly stated to thecontrary. Similarly, the discussion of any activity, work, orpublication herein is not an admission that such activity, work, orpublication was known in any particular jurisdiction.

Real-time PCR is an amplification reaction used for the quantificationof target nucleic acids in a test sample. Conventionally, skilledartisans typically view the amplification reaction as comprising threedistinct phases. First, there is a background or baseline phase, inwhich the target nucleic acid is being amplified but the signalproportional to the quantity of the target nucleic acid cannot bedetected because it is too small to be observed relative to signalsindependent of the target (sometimes called “background” or “backgroundsignal”). Next, there is a logarithmic phase in which the signal growssubstantially logarithmically because the signal is substantiallyproportional to the quantity of target nucleic acid in the amplificationreaction and is greater than the background signal. Finally, the growthin the signal slows during a “plateau” phase reflecting less thanlogarithmic amplification of the target nucleic acid. As is known in theart, the time at which the logarithmic phase crosses a threshold value,which is a value somewhat greater than the value of the backgroundsignal, is reproducibly related to the log of the concentration of thetarget nucleic acid. This prior art method is generically referred to asthe C_(t) method, perhaps so named for the Cycle at which the signalcrosses the threshold. C_(t) analysis is reasonably reproducible andaccurate, but suffers from some drawbacks, which need not be discussedhere to understand the present invention.

U.S. Pat. No. 6,303,305 discloses a method of quantification of nucleicacids employing PCR reactions. The method disclosed employs the nthderivative of the growth curve of a fluorescent nucleic acidamplification reaction. This method effectively avoids the need toperform a baseline correction, but provides no reliable method ofdetermining reactive from non-reactive samples, and does not reasonablysuggest how to use an nth derivative calculation to assess the validityof the results obtained. In addition, nucleic acid amplification signalsresulting from any artifacts in the system (e.g., crosstalk or positivebleedover—defined infra) cannot be distinguished from true positiveresponses using the methods disclosed therein and can lead to falsepositive results. However, the first derivative calculation disclosed byU.S. Pat. No. 6,303,305 provides an efficiency related value that isuseful in the context of the present invention. The skilled artisan canrefer to U.S. Pat. No. 6,303,305 for additional details relating tocalculation of a first derivative of a nucleic acid amplification signalgrowth curve. U.S. Pat. No. 6,303,305 is incorporated by reference onlyin the United States of America, and other jurisdictions permittingincorporation by reference, to the extent it discloses the calculationof the first derivative of a nucleic acid amplification growth curve.However, U.S. Pat. No. 6,303,305 does not disclose or suggest the usesof this efficiency related value described in this disclosure (below).

Co-owned U.S. Provisional Patent Application No. 60/527,389, filed Dec.6, 2003, discloses a method for analyzing a nucleic acid amplificationreaction in which the log of the signal from an amplification reactionis examined for the maximum gradient or slope. This value, which for anydata set corresponds to a point a certain period of time or number ofcycles after the initiation of the amplification reaction, is called theMGL of the reaction. The MGL is useful in certain embodiments of thepresent invention, particularly in those that distinguish qualitativelythose samples comprising little target nucleic acid from those samplesthat do not contain target nucleic acid. U.S. Patent Application No.60/527,389, filed Dec. 6, 2003 is incorporated herein by reference inits entirety.

SUMMARY OF THE INVENTION

The present invention provides a method for determining whether a samplecontains a nucleic acid of interest, for quantifying this nucleic acid,and for assessing the validity or quality of the data used to reach thepreceding qualitative and quantitative determinations.

The method of this invention method comprises contacting a sample withamplification or detection reagents or both in order to amplify thenucleic acid (as the term “amplified” is used herein). The amplificationreaction generates signals indicative of the quantity of the targetnucleic acid present in the sample, which signals are recorded atnumerous points during the amplification reaction. The signal can bemeasured and recorded as a function of time value, or in thealternative, cycle number.

Suitable “efficiency related transforms” viewed or calculated as afunction of time are determined for the amplification reaction, and thepoint in the amplification reaction of the maximum of the efficiencyrelated transform, the magnitude of the maximum of the efficiencyrelated transform, or the width (or similar parameter) of a peak in theplot of the efficiency related transform as a function of time can beused to obtain information about the reaction. This point in thereaction represents the point in time or the amplification cycle atwhich the maximum of the efficiency related transform occurs.Advantageously, the maximum of the efficiency related transform for aparticular reaction, as well as the duration and magnitude ofsubstantial changes in the calculated efficiency related transform, haveconsistently reproducible relationships to the initial concentration ofa target nucleic acid in a sample, to the reliability of the data andinformation generated by the assay, to the presence or absence of a bonafide target nucleic acid, and to other parameters of the reaction.Advantageously, these relationships hold even in the presence ofsubstantial noise and unpredictable variations in the signal(s)generated by the amplification reaction. As used herein, the term“maximum”, as applied to efficiency related transforms, is intended toinclude the minimum of the efficiency related transform when thereciprocal of the efficiency related transform is used. One can use theinverse ratio, in which, in the case of a curve, the curve will start ata value of approximately 1 in the baseline region, decrease during thegrowth region, and return approximately to one in the plateau region.The use of this transform would allow one to use the magnitude and theposition of the trough instead of the magnitude and position of the peakfor analysis. This transform is implemented in a manner that essentiallyequivalent to the ratio method in which the maximum of the efficiencyrelated transform for a particular reaction is employed.

In all embodiments, signals from the amplification reaction are measuredat intervals of time appropriate for the amplification reaction duringthe amplification reaction. These signals can be referred to astime-based or periodic measurements, such that every measurement of thesignal generated for a particular reaction can be expressed as afunction of time. In some embodiments, the amplification reaction iscyclical (e.g., as in PCR). Because cycles often have a substantiallyuniform duration, it is frequently convenient to substitute a “cyclenumber” for a time measurement. Accordingly, in some embodiments of thepresent invention, a region of data identified by one or more methods onan information processing system as described herein can correspond to acycle number. However, some cyclical amplification reactions have cyclesof non-uniform duration. For these amplification reactions, it may bepreferable to measure time in non-uniform measures. For example, thetheoretical extent of amplification in a PCR reaction having cycles ofvarying duration will be linked more directly to the number of cyclesperformed rather than the duration of the reaction. Accordingly, theskilled artisan will readily appreciate that the time-based measurementscan easily be scaled to reflect the underlying amplification reaction.As is known in the art, it is often useful to interpolate data andresults between cycle numbers, which gives rise to the concept of afractional cycle number “FCN.” Similarly, in reactions wheremeasurements are based on time, events can be measured in fractionaltime units.

In further embodiments, the invention advantageously involves a systemor method or both for analyzing a reaction sample, such as a PCRreaction sample, that uses a substantial set of available reactionkinetics data to identify a region of interest, rather than using a verylimited data set, such as where a reaction curve crosses a threshold.

In certain embodiments, an identified region can be used to determineone or more qualitative results, or quantitative data analysis results,or both. The reaction point of the maximum of the efficiency relatedtransform can be used to determine the concentration of a target nucleicacid in a sample or to determine qualitatively whether any targetanalyte is present in a test sample. These and other values can becompared with reference quantities in generally the same way that athreshold cycle number (C_(t)) or fractional threshold cycle number canbe used in the prior art.

The reaction point corresponding to the maximum of the efficiencyrelated transform can be understood as indicating or being derived froma cycle number that is located at a relatively consistent point withrespect to reaction efficiency, such as at a maximum of reactionefficiency or a region consistently related to a maximum of reactionefficiency or consistently related to some other reaction progression.Different methods can be used to determine a reaction point related to amaximum of reaction efficiency. This value can comprise adjusted FCNvalues (e.g., FCN_(MR Adj.) and FCN_(Int. Adj.)), as described below. Incertain embodiments of this invention, methods of the invention candetermine FCN values for multiple reaction signals, such as a targetand/or a control and use those values in determining reactionparameters, including, but not limited to, quantity of target nucleicacid initially present in a sample and the validity of the resultsgenerated by an amplification reaction.

The present invention can identify a value indicative of the reactionefficiency (at times, herein, generally referred to as an “efficiencyrelated value” (ERV)) at one or more regions on a signal growth curve. Aspecific efficiency related value is referred to as a MaxRatio value orMR. MaxRatio refers to one possible method for calculating an efficiencyrelated value as further discussed herein. This is one example of amethod for determining an ERV and illustrative examples herein thatrefer to MR should also be understood to include other suitable methodsfor determining an efficiency related value, including, but not limitedto, the maximum gradient of the log of the growth curve, as described inco-owned U.S. patent application Ser. No. 60/527,389, filed Dec. 6,2003, the maximum first derivative of the signal obtained from theamplification reaction (e.g., as disclosed in U.S. Pat. No. 6,303,305),and the maximum difference between two sequential signals obtained fromthe amplification reaction. Thus, this invention is involved with ananalytical method that identifies two values for a reaction curve: (1)one value related to a cycle number or time value and (2) one valueindicating an efficiency related value. The invention can use those twovalues in analysis of reaction data performed using aninformation-handling system and method of using the system. An exampleof two such values are FCN and MR specific embodiments discussed below.

This invention is also involved with a method and system that uses twovalues as discussed above that are determined from a reaction underexamination to compare that reaction to one or more criteria data sets.A criteria comparison can be used to determine and/or correct anyresults and/or quantifications as described herein. Criteria data can bederived by generating pairs of cycle number related values-efficiencyrelated values (e.g., FCN-MR pairs) from multiple calibration reactionsof known quantity or known concentration or both.

This invention also involves one or more techniques for performingefficiency analysis of reaction data. This analysis can be usedseparately from or in conjunction with the cycle number relatedvalue-efficiency related value analysis discussed herein. Efficiencyanalysis can be used to find a region of-interest for making adetermination about reaction data, such as, for comparison tocalibration data sets, in a way similar to C_(t) analysis as understoodin the art.

The present invention also provides a method for analyzing a nucleicacid amplification reaction, in which a sample containing a nucleic acidis contacted with amplification agents and placed under suitableamplification conditions to amplify a portion of the nucleic acid in thesample. During the amplification reaction, signals that are proportionalto the amount of the target nucleic acid present are periodicallymeasured at a suitable interval. Conveniently, the interval cancorrespond to the duration of a cycle for those amplification reactionsthat are cyclical. The signals are then manipulated to determine anefficiency related transform for the amplification reaction. Anysuitable efficiency related transform can be used for the invention.Efficiency related transforms preferred in the context of the presentinvention include the slope of the line, which can be determined by manytechniques, including, but not limited to, difference calculations onsequential data points, determining the first derivative of a linefitted to the growth curve of the reaction signal, and determining thegradient, slope, or derivative of the log of the growth curve (i.e., Log(growth curve)). More preferably, the efficiency related transform isthe ratio of sequential data points, sometimes referred to herein as theratio curve. When the efficiency related transform for the reaction isknown, a plot of the efficiency related transform as a function of time(preferably expressed in the units used to measure the signal) (ormathematical manipulation yielding information similar to a plot) can beused to identify a peak value. However, a plot is not required. Thewidth of the peak in the selected range of acceptable peak widths can bedetermined by any suitable technique or method. However, a preferredmethod for determining the acceptable peak width involves statisticallyanalyzing the degree of variance in peak widths obtained fromobjectively normal amplification reactions that are very similar to oreven identical to the amplification method analyzed by the method ofthis invention. In the reaction analyzed, an unknown test sample isusually used in place of samples used to characterize the amplificationreaction or an analyte assay. If the peak width of the analyzedamplification reaction falls within the prescribed range of acceptablepeak widths, the reaction is declared normal; if the peak width of theanalyzed amplification reaction does not fall within the prescribedrange of acceptable peak widths, the reaction is identified as havingprovided sub-optimal, aberrant, or otherwise questionable signals. Thewidth of the leading half of the efficiency related transform peak isevaluated. This evaluation is a more forgiving measurement ofamplification reaction validity, and therefore may be preferred in someinstances, but generally not in all instances.

The invention further involves an information system and/or program ableto analyze captured data. Data can be captured as image data fromobservable features of the data, and the information system can beintegrated with other components for capturing, preparing, and/ordisplaying sample data. Representative examples of systems in which theinvention can be employed include, but are not limited to, the BioRad®i-Cycler®, the Stratagene® MX4000®, and the ABI Prism 7000® systems.Similarly, the present invention provides a computer product capable ofexecuting the method of this invention.

Various embodiments of the present invention provide methods and/orsystems that can be implemented on a general purpose or special purposeinformation handling system by means of a suitable programming language,such as Java, C++, C#, Cobol, C, Pascal, Fortran, PL1, LISP, assembly,etc., and any suitable data or formatting specifications, such as HTML,XML, dHTML, TIFF, JPEG, tab-delimited text, binary, etc. For ease ofdiscussion, various computer software commands useful in the context ofthe present invention are illustrated in MATLAB® commands. The MATLABsoftware is a linear algebra manipulator and viewer package commerciallyavailable from The Mathworks, Natick, Massachusetts (USA). Of course, inany particular implementation (as in any software development project),numerous implementation-specific decisions can be made to achieve thedeveloper's specific goals, such as compliance with system-relatedand/or business-related constraints, which will vary from oneimplementation to another. Moreover, it will be appreciated that such adevelopmental effort might be complex and time-consuming, but wouldnevertheless be a routine undertaking of software engineering for thoseof ordinary skill in the art having the benefit of this disclosure.

The invention will be better understood with reference to the followingdrawings and detailed descriptions. For purposes of clarity, thisdiscussion refers to devices, methods, and concepts in terms of specificexamples. However, the invention and aspects thereof may haveapplications to a variety of types of devices and systems.

Furthermore, it is well known that logic systems and methods such asthose described herein can include a variety of different components anddifferent functions in a modular fashion. Different embodiments of theinvention can include different combinations of elements and functionsand may group various functions as parts of various elements. Forpurposes of clarity, the invention is described in terms of systems thatinclude many different components and combinations of novel componentsand known components. No inference should be taken to limit theinvention to combinations requiring all of the novel components in anyillustrative embodiment of this invention.

As used herein, “the invention” should be understood to include one ormore specific embodiments of the invention (unless explicitly indicatedto the contrary). Many variations according to the invention will beunderstood from the teachings herein to those of ordinary skill in theart.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plot of discrete captured reaction data values from 43readings (e.g., cycles) taken from a nucleic acid amplification reactionthat can be used in an analysis method according to embodiments of thisinvention.

FIG. 2 is a plot illustrating captured reaction data showing target andcontrol data sets that have been normalized according to embodiments ofthis invention.

FIG. 3 is a plot illustrating reaction data showing target and controldata that have been scaled according to embodiments of this invention.

FIG. 4 is a plot illustrating captured reaction data showing target andcontrol data after digital filtering according to embodiments of thisinvention.

FIG. 5 is a plot illustrating captured reaction data showing target andcontrol data with slope values removed according to embodiments of thisinvention.

FIG. 6 is a plot illustrating ratio transform of reaction target andcontrol data according to embodiments of this invention.

FIG. 7 is a plot illustrating shifted ratio transform of reaction targetand control data according to embodiments of this invention.

FIG. 8 is a plot illustrating interpolated transformed reaction datashowing target and control data that have been interpolated according toembodiments of this invention.

FIG. 9 is a plot illustrating interposed reaction data showingidentification of the FCN and MR points according to embodiments of thisinvention.

FIG. 10 is a flow chart for performing a characterization of reactiondata according to embodiments of this invention.

FIG. 11 is a plot illustrating methods for determining criteria dataaccording to embodiments of this invention.

FIG. 12 is a plot illustrating two sets of reaction data that illustratehow reaction curves for same concentration initial samples can vary dueto different reaction anomalies.

FIG. 13 illustrates peak efficiency calculations for the data sets inFIG. 12. The figure illustrates the desirability of using an offsetefficiency transform according to specific embodiments of the presentinvention.

FIG. 14 illustrates data for an HIV assay run with eight replicates ofknown concentration samples at 50, 500, 5,000, 50,000, 500,000 and5,000,000 copies per mL.

FIG. 15 is a plot illustrating four linear standard curves generatedfrom three-point calibration data using four different cycle numberrelated values (e.g., FCN, FCN2, FCN_(MR Adj.), and FCN_(Int. Adj.))according to embodiments of this invention.

FIG. 16 compares calculated concentrations to known concentrations forthe data illustrated in FIG. 14 using the four curves illustrated inFIG. 15 according to embodiments of this invention.

FIG. 17 illustrates results using a one-point calibration according toembodiments of this invention.

FIG. 18 illustrates experimental HBV results using MR analysis with aone-point calibration according to embodiments of this invention.

FIG. 19 illustrates experimental HBV results using MR analysis andFCN_(MR adj.) with a one-point calibration according to embodiments ofthis invention.

FIG. 20 illustrates experimental HBV results using C_(t) analysis and aone-point calibration according to embodiments of this invention.

FIG. 21 illustrates experimental HIV results using MR analysis andone-point calibration, e.g. using 10³ and 10⁷ copies/mL responses ascalibrators, according to embodiments of this invention.

FIG. 22 is a plot illustrating two types of criteria data according toembodiments of this invention wherein the lower horizontal linerepresents criteria data suitable for differentiating negative reactionsfrom positive reactions.

FIG. 23 is a plot illustrating FCN-MR for HIV data from 50 copies/mL to5,000,000 copies/mL analyzed by a statistics software package to apply acurve fit to the data and to determine confidence intervals according toembodiments of this invention.

FIG. 24 is a plot illustrating internal control data analyzed by astatistics software package to determine confidence intervals accordingto embodiments of this invention.

FIG. 25 is a flow chart illustrating a logic analysis tree forassessment of assay validity through analysis of pairs of cycle numberrelated value—efficiency related value for both the internal control andthe target amplification reactions according to embodiments of thisinvention.

FIG. 26 is a flow chart illustrating a logic analysis tree for reportingtarget results with validity criteria assessment using the pairs ofcycle number related value—efficiency related value according toembodiments of this invention.

FIG. 27 illustrates the calculation of peak width measurements accordingto embodiments of this invention.

FIG. 28 illustrates experimental HIV results using the full peak widthmeasurement according to embodiments of this invention.

FIG. 29 illustrates experimental HIV results using the full peak widthmeasurement to identify an abnormal response according to embodiments ofthis invention.

FIG. 30 illustrates an example of a user interface displaying an FCN-MRplot according to embodiments of this invention.

FIG. 31 illustrates an example of a user interface displaying a shiftedratio plot according to embodiments of this invention.

FIG. 32 is a block diagram showing a representative example of a logicdevice in which various aspects of the present invention may beembodied.

DETAILED DESCRIPTION OF THE INVENTION

As used herein, the expression “efficiency related value” means a valuethat has a consistent relationship to the efficiency of an amplificationreaction. The expression “efficiency related transform” means amathematical transformation involving the response in an amplificationreaction that is used to determine an efficiency related value. Theexpression “reaction point” means a point during a reaction at which anefficiency related value occurs. The reaction point can be a point intime measured from the beginning of the reaction. Alternatively, thereaction point can be a point that denotes a cycle measured from thebeginning of the reaction. The term “derivative” means the slope of acurve at a given point in the curve.

The present invention is directed to the analysis of a sample containingan analyte. The analyte can be a nucleic acid. In the context of thepresent invention, copies of a portion of the analyte are made(hereinafter “amplified”) in a manner that generates a detectable signalduring amplification. The signal is indicative of the progress of theamplification reaction, and preferably is related either to the quantityof analyte and copies of the analyte present in a test sample, or isrelated to the quantity of the copies of the analyte produced by thereaction. The amplification is preferably configured to allowlogarithmic accumulation of the target analyte (e.g., as in a PCRreaction), and in a more preferred embodiment, the amplification is aPCR reaction in which data are collected at regular time intervalsand/or at a particular point in each PCR cycle.

Many systems have been developed that are capable of amplifying anddetecting nucleic acids. Similarly, many systems employ signalamplification to allow the determination of quantities of nucleic acidsthat would otherwise be below the limits of detection. The presentinvention can utilize any of these systems, provided that a signalindicative of the presence of a nucleic acid or of the amplification ofcopies of the nucleic acid can be measured in a time-dependent orcycle-dependent manner. Some preferred nucleic acid detection systemsthat are useful in the context of the present invention include, but arenot limited to, PCR, LCR, 3SR, NASBA, TMA, and SDA.

Polymerase Chain Reaction (PCR) is well-known in the art and isessentially described in Saiki et al., Science 230; 1350-1354 (1985);Saiki et al., Science 239:487-491 (1988); Livak et al., U.S. Pat. Nos.5,538,848; 5,723,591; and 5,876,930, and other references. PCR can alsobe used in conjunction with reverse transcriptase (RT) and/or certainmultifunctional DNA polymerases to transform an RNA molecule into a DNAcopy, thereby allowing the use of RNA molecules as substrates for PCRamplification by DNA polymerase. Myers et al. Biochem. 30: 7661-7666(1991)

Ligation chain reactions (LCR) are similar to PCR with the majordistinguishing feature that, in LCR, ligation instead of polymerizationis used to amplify target sequences. LCR is described inter alia inBackman et al., European Patent 320 308; Landegren et al., Science241:1077 (1988); Wu et al., Genomics 4:560 (1989). In some advancedforms of LCR, specificity can be increased by providing a gap betweenthe oligonucleotides, which gaps must be filled in by template-dependentpolymerization. This can be especially advantageous if all four dNTPsare not needed to fill the gaps between the oligonucleotide probes andall four dNTPS are not supplied in the amplification reagents.Similarly, rolling circle amplification (RCA) is described by Lisby,Mol. Biotechnol. 12(1):75-99 (1999)), Hatch et al., Genet. Anal.15(2):35-40 (1999) and others, and is useful in the context of thepresent invention.

Isothermal amplification reactions are also known in the art and usefulin the context of the present invention. Examples of isothermalamplification reactions include 3SR as described by Kwoh et al., Proc.Nat. Acad. Sci. (USA) 86: 1173-1177 (1989) and further developed in theart; NASBA as described by Kievits et al., J. Virol. Methods 35:273-286(1991) and further developed in the art; and Strand DisplacementAmplification (SDA) method as initially described by Walker et al.,Proc. Nat. Acad. Sci. (USA) 89:392-396 (1992) and U.S. Pat. No.5,270,184 and further developed in the art.

Thus, many amplification or detection systems requiring only that signalgains indicative of the quantity of a target nucleic acid can bemeasured in a time-dependent or cycle-dependent manner are useful in thecontext of the present invention. Other systems having thesecharacteristics are known to the skilled artisan, and even though notdiscussed above, are useful in the context of the present invention.

Analysis of the data collected from the amplification reaction canprovide answers to one or more of the following questions:

-   -   (1) Was the target sequence found?    -   (2) If yes, what was the initial level or quantity of the target        sequence?    -   (3) Is the result correct?    -   (4) Did the reaction series run correctly?    -   (5) Was there inhibition of the desired or expected reaction?    -   (6) Is the sample preparation recovery acceptable?    -   (7) Is the calibration to any reference data, if used, still        valid?

According to some embodiments of this invention, one or more of thesequestions can be answered by identifying a region of interest (e.g., anFCN) and an efficiency related value (e.g., an MR) of a target and/orinternal control reaction. In other embodiments, one or more of thesequestions can be answered by comparing such values to data sets hereinreferred to as criteria data, criteria curves, and/or criteria datasets. In additional embodiments, one or more of these questions can beanswered by comparing such values obtained for an internal control,e.g., a 2^(nd) amplification control reaction, in the same reactionmixture as its criteria data. In still further embodiments, one or moreof these questions can be answered by comparing such values obtained forthe target reaction to such values obtained for an internal controlreaction in the same reaction mixture as their respective criteria data.

For clarity, the invention will be illustrated with reference toreal-time PCR reactions, which are one class of measuring and monitoringtechniques of high interest in automated and manual systems fordetecting and quantifying human nucleic acids, animal nucleic acids,plant nucleic acids, and nucleic acids of human, non-human animal, andplant pathogens. Real-time PCR is also well adapted to detection ofbio-warfare agents and other living or viral organisms in theenvironment. Real-time PCR combines amplification of nucleic acid (NA)sequence targets with substantially simultaneous detection of theamplification product. Optionally, detection can be based on fluorescentprobes or primers that are quenched or are activated depending on thepresence of a target nucleic acid. The intensity of the fluorescence isdependent on the concentration or amount of the target sequence in asample (assuming, of course, that the quantity of the target is above aminimal detectable limit and is less than any saturation limit). Thisquench/fluoresce capability of the probe allows for homogeneous assayconditions, i.e., all the reagents for both amplification and detectionare added together in a reaction container, e.g., a single well in amulti-well reaction plate. Electronic detection systems, target-capturebased systems, and aliquot-analysis systems and techniques are otherforms of detection systems useful in the context of the presentinvention so long as a given system accumulates data indicative of thequantity of target present in a sample during various time points of atarget amplification reaction.

In PCR reactions, the quantity of target nucleic acid doubles at eachcycle until reagents become limiting or are exhausted, there issignificant competition, an inadequate supply of reactants, or otherfactors that accumulate over the course of a reaction. At times duringwhich a PCR reaction causes doubling (exactly) of the target in aparticular cycle, the reaction is said to have an efficiency (e) of 1(e.g., e=1). After numerous cycles, detectable quantities of the targetcan be created from very small and initially undetectable quantity oftarget. Typically, PCR cycling protocols consist of between around 30-50cycles of amplification, but PCR reactions employing more or fewercycles are known in the art and useful in the context of the presentinvention.

In the real-time PCR reactions described below to illustrate the presentinvention, the reaction mixture includes an appropriate reagent cocktailof oligonucleotide primers, fluorescent dye-labeled oligonucleotideprobes capable of being quenched when not bound to a complementarytarget nucleic acid, amplification enzymes, deoxynucleotidetriphosphates (dNTPs), and additional support reagents. Also, a secondfluorescent dye-labeled oligonucleotide probe for detection of anamplifiable “control sequence” or “internal control” and a “referencedye”, which optionally may be attached to an oligonucleotide thatremains unamplified throughout a reaction series, can be added to themixture for a real-time PCR reaction. Thus, some real-time PCR systemsuse a minimum of three fluorescent dyes in each sample or reactioncontainer (e.g., a well). PCR systems using additional fluorescentprobe(s) for the detection a second target nucleic acid are known in theart and are useful in the context of the present invention.

Systems that plot and display data for each of one, or possibly more,reactions (e.g., each well in a multi-well plate) are also useful in thecontext of the present inventions. These systems optionally calculatevalues representing the fluorescence intensity of the probe as afunction of time or cycle number (C_(N)) or both as a two-dimensionalplot (y versus x). Thus, the plotted fluorescence intensity canoptionally represent a calculation from multiple dyes (e.g., the probedye and/or the control dye normalized by the reference dye) and caninclude subtraction of a calculated background signal. In PCR systems,such a plot is generally referred to as a PCR amplification curve andthe data plotted can be referred to as the PCR amplification data.

In PCR, data analysis can be made difficult by a number of factors.Accordingly, various steps can be performed to account for thesefactors. For example, captured light signals can be analyzed to accountfor imprecision in the light detection itself. Such imprecision can becaused by errors or difficulties in resolving the fluorescence of anindividual dye among a plurality of dyes in mixture of dyes (describedbelow as “bleedover”). Similarly, some amount of signal can be present(e.g., “background signal”) and can increase even when no target ispresent (e.g., “baseline drift”). Thus, a number of techniques forremoving the background signal, preferably including the baseline drift,trend analysis, and normalization are described herein and/or are knownin the art. These techniques are useful but are not required in thecontext of the present invention. (Baseline drift or trending can becaused by many sources, such as, for example, dye instability, lampinstability, temperature fluctuations, optical alignment, sensorstability, or combinations of the foregoing. Because of these factorsand other noise factors, automated methods of identifying and correctingthe baseline region are prone to errors.)

Typically in PCR, the answers of interest are generally determined froma growth curve, which characteristically starts out as nearly flatduring the early reaction cycles when insufficient doubling has occurredto cause a detectable signal, and then rises exponentially until one ormore reaction limiting conditions, such as exhaustion of one or morereactants, begins to influence the amplification reaction or thedetection process.

A number of methods have been proposed and have been used in researchand other settings to analyze PCR-type reaction data. Typically, thesemethods attempt to detect when the reaction curve has reached aparticular point, generally during a period of exponential ornear-exponential signal growth (also known as “the log-linear phase”).While not wishing to be bound by any theory, the inventors believe thatthe earliest point(s) in which the log linear phase can be observedabove the baseline or background signal provides the most usefulinformation about the reaction and that the slope of the log-linearphase is a reflection of the amplification efficiency. Some prior artreferences erroneously suggest that for the slope to be an indicator ofreal amplification (rather than signal drift), there has to be aninflection point, which is the point on the growth curve where thelog-linear phase ends. The inflection point can also represent thegreatest rate of change along the growth curve. In some reactions whereinhibition occurs, the end of the exponential growth phase may occurbefore the signal emerges from the background.

In running a PCR analysis, it is generally desired to determine one ormore assay results regarding the initial amount/concentration of thetarget molecules. For discussion purposes, results may be expressed byanswers to at least one of four questions:

(1) Was the target molecule present at all in the initial sample (e.g.,a positive/negative detection result)?

-   -   (2) What was the absolute quantity of the initial target        present?    -   (3) What is the confidence (e.g., sometimes expressed as a        confidence value that the answers to questions 1 or 2 are        correct)?    -   (4) What is the relative amount of the target present in two        different samples?        A number of methods have been proposed and can be used in        research and other settings to answer one or more of these        questions.

Data for PCR reactions is often collected one time in each cycle foreach dye that is measured (i.e., fluorescence determined) in a reaction.While such data is useful in the context of the present invention, moreprecise quantification can be carried out by interpolation between thedata points acquired at each cycle. In this way, the data can beanalyzed to generate “fractional cycle numbers”, and points of interestcan be determined to be coincident with a particular cycle number or ata reaction point between any pair of cycle numbers.

One problem with methods that rely on thresholds, particularly indiagnostic settings where it is desirable to fix thresholds, is thattheses methods can be susceptible to errors due to the presence of noisefactors, particularly systematic noise factors, such as, for example,“crosstalk” and “bleedover”. Crosstalk can generally be understood asoccurring when a signal from an assay in one location (such as one wellin a multi-well plate) causes an anomaly in a signal in a different,usually adjacent assay location. Bleedover can generally be understoodas occurring in situations where more than one signal or data set isdetected from the reaction. While detection dyes for a reaction areselected to be largely independent from each other and to haveindividual fluorescence emission spectra, the emission spectra sometimesoverlap such that the emission spectrum from one dye will bleedover intothe emission spectrum of a different dye.

Both crosstalk and bleedover can have the effect of either increasing ordecreasing the calculated measurement of interest. Furthermore, in bothcases, there can be situations where the curve itself can have ananomaly due to either or both of these phenomena. Systematic noisefactors such as crosstalk and bleedover can be especially difficult todeal with when performing a baseline correction.

In some systems of the prior art, in order to detect low-level signalsfor either qualitative results or quantitative results, a low thresholdis generally required. However, the use of a low threshold causesdiscrimination between a false positive signal due to crosstalk and acorrect positive signal to be particularly difficult, because either cancause the PCR curve to rise above an amplification threshold, therebysuggesting that a target analyte is present. Positive and negativebleedover can also present problems. Positive bleedover can produce afalse-positive results or cause falsely elevated estimates of theinitial quantity of target in a sample, while negative bleedover cancause falsely depressed estimates of the initial quantity of target in asample or falsely indicate the absence of a target in a test sample.

The method or system of this invention can reproducibly identify aregion in a reaction curve or data, preferably using an informationprocessing system, which can then be used to provide results based onthe amplification reaction data. The invention can identify this regionregardless of the base level of the signal, even in the presence ofsubstantial noise. The invention can furthermore identify a value thatis representative of efficiency at that region. This value can be usedin determining primary results or in adjusting results or in determiningconfidence values as described herein, or all of the foregoing.

The invention can be illustrated by a specific example, shown below. Inthis example, an information processing system is used to analyze datarepresenting the growth curve of an amplification reaction. In theamplification, a “peak” is generated by one step in the data analysis.The location of this peak (measured in time units or in cycles from theinitiation of the amplification reaction) is referred to as thefractional cycle number (FCN) and the maximum value of the peak isreferred to as the ERV (efficiency related value). These values can beused in a method to identify an efficiency related value region and todetermine an efficiency related value at this peak. Both of these valuescan be understood as being derived from a method that analyzes the shapeof the reaction curve regardless of the intensity of the amplificationsignal, which intensity of amplification signal can vary from reactionto reaction and from instrument to instrument, despite starting withidentical samples. The reaction curve is a representation of thereaction wherein a signal substantially indicative of the quantity oftarget in a reaction is plotted as a function of time or, whenappropriate, cycle number. The FCN can be understood as beingconsistently related to a point of maximum growth efficiency of areaction curve, and the ERV can be understood as being consistentlyrelated to the efficiency at that point.

In some embodiments of this invention, analytical methods canoptionally, and advantageously, be employed without use of baselinecorrection. In some systems and methods of this invention, a referencedye is not needed.

The present invention allows objective quantification of the quantity ofa target present in a test sample without the need to calculate asubjective and variable threshold or a C_(t) value, as employed in sometechniques of the prior art. Furthermore, the invention can useinformation that is available for determining the degree of inhibitionin a reaction by analyzing the shape of the PCR amplification curve,including data that previously has generally been ignored, such as datain cycles after a C_(t).

General methods for generating and using data pairs determined fromreaction curve data will be understood from the examples below. Forclarity, these examples refer to a specific set of data and specificfunctions for analyzing that data, though the invention is not limitedto the examples discussed.

EXAMPLE 1 Captured Data

By way of example, a typical real-time PCR reaction detection systemgenerates a data file that stores the signal generated from one or moredetection dyes. FIG. 1 illustrates a plot of captured reaction data thatcan be used in an analytical method according to the present invention.In this example, one dye signal (DYE1) provides the captured targetdata, another dye signal (DYE2) provides captured internal control data,and a further dye signal (DYE3) provides optional captured referencedata. These data represent data from a single reaction, taken from astandard output file. This particular plot can be understood torepresent initial data to which some type of multi-component algorithmhas been applied. In this plot, the x-axis provides an indication ofcycle number (e.g., 1 to 45) and the y-axis indicates dye intensitydetected, in relative fluorescence units. In this figure, the threedifferent capture data sets are illustrated as continuous curves.However, the actual captured data values are generally discrete signalvalues captured at each cycle number. Thus, an initial data set asillustrated in FIG. 1 may consist of three sets (target, control, andreference) of suitable discrete values (e.g., about 50 values in thiscase).

EXAMPLE 2 Normalization

Although optional, normalization can be performed on the captured datain several different ways. One method involves dividing the target andcontrol values at each cycle reading by the corresponding reference dyesignal. Alternatively, the divisor can be the average reference valueover all cycles or an average over certain cycles. In anotheralternative embodiment, the divisor can be the average of the target dyeor the control dye or the target dye and the control dye over one ormore earlier (baseline) cycles, when no amplification signal isdetected. Any known normalization method can be employed in a dataanalysis. The invention can be used with data that has already beennormalized by a PCR system. FIG. 2 is a plot of captured reaction datashowing target and control data sets that have been normalized accordingto the present invention. In this example, as a result of thenormalization, the y-axis scale represents a pure number. In this case,the number is between about 0 and 9. Other normalization methods areknown in the art and can convert this number to between about 0 and 100or to any other desired range.

Because normalization is optional, the present invention can be used toanalyze reaction data without the use of a normalization or referencedye. Alternatively, the target signal or the control signal or both canbe used for normalization.

EXAMPLE 3 Scaling

Scaling is optional but can be performed to make it easier for a humanoperator to visualize the data. Scaling does not affect analyticalresults. Scaling can be carried out in addition to normalization, in theabsence of normalization, or before or after normalization.

One method of scaling involves dividing each data set value by theaverage of the values during some early cycles, generally in thebaseline region before any positive data signal is detected. In thisexample, readings 4 through 8 were averaged and normalization wasperformed first. FIG. 3 is a plot of reaction data showing target andcontrol data that have been scaled. In this example, scaling forces theearly values of the target and control to one, and because the earlyvalues are less than one, the division forces the later values toslightly larger pure numbers.

EXAMPLE 4 Digital Filtering

One or more digital filtering methods can be applied to the captureddata to “clean up” the signal data sets and to improve the signal tonoise ratio. Many different filtering algorithms are known. The presentinvention can employ a four-pole filter with no zeros. This eliminatesthe potential for overshoot of the filtered signal. As an example, thiscan be implemented with the MATLAB function “filtfilt” provided with theMATLAB Signal Processing Toolbox, which both forward and backwardfilters to eliminate any phase lag (time delays). An example ofparameters and MATLAB function call is as follows:

-   -   b=0.3164;    -   a=[1.0000-1.0000 0.3750-0.0625 0.0039];    -   data(:,:,assay)=filtfilt(b,a,data(:,: ,assay));    -   data(:,:,ic)=filtfilt(b,a,data(:,:,ic));

In this example, “b” and “a” contain the filter coefficients.“data(:,:,assay)” and “data(:,:,ic)” contain the captured data that mayor may not have been normalized, scaled, or both. In this case, thefiltered data is both normalized and scaled. FIG. 4 is a plot ofcaptured reaction data showing target and control data after digitalfiltering. The values are not changed by the digital filtering, but thedata set is “smoothed” somewhat.

EXAMPLE 5 Slope Removal/Baselining

An optional slope removal method can be used to remove any residualslope that is present in the early baseline signal before any detectableactual signal is produced. This procedure may also be referred to asbaselining, but in some embodiments, the offset is not removed, only theslope. According to this invention, for slope removal, both the target(DYE1) and control (DYE2) signals are examined simultaneously. Whicheversignal comes up first defines the forward regression point, and themethod generally goes back 10 cycles. If 10 cycles back is before cycle5, then cycle 5 is used as the initial regression point to avoid anyearlier signal transients. A linear regression line is calculated usingthe signal data between these points and the slope of the regression foreach dye is subtracted from that dye's signal. In this case, the sloperemoval is applied to the normalized, scaled, and filtered datadiscussed above. FIG. 5 is a plot of captured reaction data showingtarget and control data with slope values removed. In each of thesefigures, very little slope was present in early cycles; therefore, theslope removal does not substantially affect the captured data values.

EXAMPLE 6 Transform Calculation

An embodiment of the method of this invention is the MaxRatio method. Inthis method, the ratio between sequential measurements is calculated,thereby yielding a series of ratios, each of which can be indexed to atime value or cycle number. Many suitable means of calculating theseratios exist, and any suitable means can be used. The simplest way ofperforming this ratio calculation utilizes the following function:${{Ratio}(n)} = \frac{s\left( {n + 1} \right)}{s(n)}$where n represents the cycle number and s(n) represents the signal atcycle n. This calculation provides a curve that starts at approximately1 in the baseline region of the response, increases to a maximum duringthe growth region, and returns to approximately 1 in the plateau region.A MATLAB expression that performs this calculation efficiently is thefollowing:Ratio=s(2:end,:)./s(1:end−1,:),

-   -   where “s” represents the signal response matrix, with each        column representing a separate response.

FIG. 6 shows an example of this ratio transform. Because of theintrinsic background fluorescence, the ratio does not reach 2 as wouldbe expected of a PCR reaction if the signal were doubling. Regardless,the magnitude of the peak is independent of multiplicative intensityvariations and is proportional to the rate of growth or efficiency atthat point. The method of calculating ratios is simple and efficientlycalculated. Other equivalent calculations could be made. An examplewould involve calculating the forward and reverse ratios and thenaveraging them. On can use the inverse of the ratio, in which case thecurve will begin at a value of approximately 1 in the baseline region,decrease in the growth region, and return to a value of approximately 1in the plateau region. One would then use the magnitude and location ofthe trough instead of a peak for analysis. This transform can beimplemented in a manner essentially equivalent to the ratio method.

Although the MaxRatio algorithm is usable as described, it is convenientto shift the curve by subtracting a constant, e.g., about one (1), fromeach point. This operation provides a transformation of the originalresponse, which starts near zero in the baseline region, rises to a peakin the growth region of the curve, and returns near zero in the plateauregion. This shifted ratio calculation is described by the followingfunction: ${{Ratio}(n)} = {\frac{s\left( {n + 1} \right)}{s(n)} - 1.}$FIG. 7 shows the output of this shifted ratio calculation. The reactionpoint and magnitude of the peak of the shifted ratio curve is thendetermined. The reaction point (i.e., distance along the x-axis)specifies the FCN value of the MR and the magnitude specifies theefficiency related value MR (Maximum of the Ratio).

EXAMPLE 7 Interpolation

In order to enhance cycle number resolution, an interpolation can beperformed. Many ways of accomplishing this operation are known in theart. One method of interpolating in the context of the invention iscubic spline interpolation, which provides a smooth interpolation, sothat even the second derivative of the captured data sets will becontinuous. The invention can be used to interpolate the entiredata'series. The invention can be used to determine a region of interestand then to interpolate only in that region to achieve sub-periodic, orsub-cycle, resolution. An example of a MATLAB command for performing acubic spline interpolation is as follows:out=interp1 (x,in,x 2, ‘spline’)where “x” represents the period (or cycle) numbers (1,2,3 . . . ), “in”represents the uninterpolated signal at those cycles, “x2” representsthe higher resolution period (or cycle) vector (1.00, 1.01, 1.02, . . .) and “out” represents the interpolated signal that corresponds to thefractional cycles in “x2”.

FIG. 8 is a plot of captured reaction data showing target and controldata that have been interpolated to provide function continuity. As aresult of an interpolation, the number of values in the data set willgenerally increase substantially, for example from 43 values to 4201values.

It should be understood that the steps described above can be performedin different orders, such as, for example, filtering first, followed bybaselining before scaling. However, if the interpolation is performedbefore the ratio calculation, care must be taken to select theappropriate interpolated response values for the ratio calculation. Itis important that the interval between ratio values remain the same.Thus, if cycles are used as the period of measurement, and interpolationincreases the time resolution to 0.01 cycles, then the shifted ratio atx=2.35 would be R=s(3.35)/s(2.35)−1.

EXAMPLE 8 Finding Peaks to Determine FCN and ERV (e.g., MR) of Targetand Control

Another step is to select peaks in the data series. This operationinvolves the steps of (1) finding local peaks and (2) selecting fromlocal peaks one or more peaks for further analysis, optionally usingcriteria data (defined infra).

A peak-finding algorithm identifies where the slope of the curve changesfrom positive to negative, which represents a local maximum. Thealgorithm identifies the locations and the magnitude of the peaks. Anexample of a MATLAB function to do this calculation is as follows:function [ind,peaks]=findpeaks(y)

-   -   % FINDPEAKS Find peaks in real vector.    -   % ind=findpeaks(y) finds the indices (ind) which are    -   % local maxima in the sequence y.    -   % [ind,peaks]=findpeaks(y) returns the value of the

% peaks at these locations, i.e. peaks=y(ind); y = y(:)′; switchlength(y) case 0  ind = [ ]; case 1  ind = 1; otherwise  dy = diff(y); not_plateau_ind = find(dy˜=0);  ind = find( ([dy(not_plateau_ind) 0]<0)&   ([0 dy(not_plateau_ind)]>0) );  ind = not_plateau_ind(ind); end ifnargout > 1  peaks = y(ind); end

FIG. 9 is a of an efficiency calculation showing identified FCN and MRvalues of the target and internal control dyes and a criteria curveaccording to embodiments of the present invention. For the target data,FINDPEAKS located one peak at cycle axis x=19.42 with a magnitude of0.354. For the internal control data, FINDPEAKS found peaks at: x=2.03,5.29, 7.67, 12.83, 22.70, 37.86, with respective magnitudes 0.0027,0.0027, 0.0022, 0.0058, 0.1738, 0.0222.

EXAMPLE 9 Selecting Peaks to Determine FCN and ERV (e.g., MR) of Targetand Control

In the method discussed above, a number of local maximum peaks are oftenidentified for both the target data and the control data. Variousmethods can be used for selecting which of these local maximum peakswill be used for determining an FCN and ERV.

Typically, and in particular during well-behaved reactions, the highestpeak or maximum peak is selected. In many situations, this selectionprovides the most reproducible reaction point from which to performfurther calculations as discussed herein. However, in some situations, afirst peak, or first peak above a particular cutoff or after aparticular number of cycles is preferable. Thus, in particular examples,a Max Peak or First Peak selection can be employed where Max Peak findsthe largest peak in the shifted ratio curve while First Peak finds thefirst peak that is higher than some selected value.

Once criteria data are determined, these data can also be used todetermine which peak to select for an ERV determination during actualoperation, particularly for weak or noisy signals.

In FIG. 9, for example, for the DYE2 data, the peak-finding algorithmfound six local peaks, but the fifth peak was the maximum peak and wasalso the only one that was above the criteria curve. Thus, in thisexample, an FCN determined for DYE2 is 22.70 and the MR determined forDYE 2 is 0.1738.

An information appliance or system apparatus can also be used to performthe methods of this invention. FIG. 10 is a flow chart for performing areaction data characterization according to embodiments of the presentinvention. Further details of this general method will be understoodfrom the discussion below.

The analytic methods described herein can be applied to reactionscontaining either known or unknown target concentrations. In oneembodiment, known target nucleic acid concentrations will be included incalibration wells in a reaction carried out in a multi-well reactionplate, and the ERV and value of the reaction point will be used fromthese known concentration samples to perform quantification. Knownconcentrations may also be used to develop criteria data as furtherdescribed herein.

EXAMPLE 10 Determining Criteria Curve/Criteria Data Sets

In other embodiments, efficiency related values (e.g., MR values) can beplotted as a function of their reaction point values (FCN values) for anumber of data sets of known concentration in order to generate acharacteristic criteria curve for a particular assay. The criteria curveis characteristic of a particular assay formulation and detectionprotocol and can be used to reliably determine positive/negativeresults, to determine whether a particular result should be discarded asunreliable, to determine a confidence measure of a result, or anycombination of the foregoing. In general, pairs of reaction data thatlie below a criteria curve indicate non-reactive samples, ornon-functional reactions, such as reactions encountering significantinhibition.

Criteria data can be used to select which peaks to report or to use inreaction analysis, or both. Criteria data provide an automatic andreliable method for discriminating between negative results (e.g.,target not present at all) and results showing low amount of target.

FIG. 11 is a plot in which the MR of six sets of reactions of knownconcentration (i.e., standards or calibrators) and one set of negativereactions are plotted as a function of the calculated FCN value of theMR value. This plot allows a criteria curve to be selected. A criteriacurve, which was described previously, is any curve or line thatseparates positive results from negative results. The criteria curve ispreferably selected so that it is relatively close to and above thenegative reaction data (in the x-y space of the plot). In FIG. 11, pairsof MR-FCN data from a number of samples of known concentrationsdetermined under the same or similar assay conditions are plottedtogether with pairs of MR-FCN data from samples that do not contain thetarget of the assay, which samples are also referred to as negatives.Although the negatives should exhibit no amplification response, theanalytical method does determine an MR-FCN data pair for these samples.These data for negative samples usually correspond to noise drivenmaxima on the response output, which is generally a random response. TheMR value determined from noise is very low and far removed from theresponses from samples of known concentrations. MR-FCN pairs fornegative reactions can cluster if there is a systematic noise source,such as bleedover, in which case the MR-FCN pairs may falsely appear tobe positive reaction signals. In characterizing the MR-FCN response oftrue positives versus true negatives, one can identify a clear region ofseparation between these two sets of data, which is represented by thebroken line or curve in FIG. 11, the criteria curve. In this figure,each circle represents a FCN-MR data pair. In this case, each of theclusters of circles represents multiple responses at knownconcentrations of the target. There are eight different replicates atsix known concentrations within this example. From the right of theplot, for example, these known concentrations can representconcentrations of 50 copies/ml, 5×10² copies/ml, 5×10³ copies/ml, 4×10⁴copies/ml, 5×10⁵ copies/ml, and 5×10⁶ copies/ml. These criteria dataclusters can be used to generate a criteria curve.

Multiple, relatively simple criteria data sets can be used to providecharacteristic criteria curves for a number of assays. One usefulapproach involves taking the mean of the MR values for the set ofnegative responses and adding to this value a multiple of the standarddeviation of the MR values for the negative responses. For the exampleshown in FIG. 11, the criteria curve was set to be a horizontal lineequal to the mean plus 10 standard deviations of the MR values for thenegative responses. The criteria value in this example was calculated tobe about 0.026. In some systems, other considerations can makemodification of the criteria value (e.g., an FCN-MR value) desirable toaccount for potential signal anomalies, such as, for example, crosstalkor positive bleedover. Crosstalk can result from signal in a positivewell of a multi-well instrument and influence the signal from adifferent well. As much as 2% crosstalk has been observed in certaininstruments. For this reason, the criteria may be increased so as toavoid classifying true negative samples as positive samples. For theassay data represented in FIG. 11, the highest MR values for positiveassays are about 0.50. Two percent of this value is 0.010. Increasingthe criteria by 0.010 should eliminate false positives due to crosstalk.Because the highest MR values in this assay only occur with samples ofhigher concentration that have smaller FCN values, the criteria may beincreased only at smaller FCN values, where crosstalk is likely tooccur. This modified criteria set can be described by a series of datapairs (X_(n), Y_(n)), which describe a multi-element curve. For example,the modified criteria curve shown in FIG. 11 can be specified by thecriteria data set:(X ₁ , Y ₁)=(1, 0.036)(X ₂ , Y ₂)=(20, 0.036)(X ₃ , Y ₃)=(25, 0.026)(X ₄ , Y ₄)=(45, 0.026)As a further example, the criteria curve shown in FIG. 10 can bespecified by the criteria data set:(X ₁ , Y ₁)=(1, 0.10)(X ₂ , Y ₂)=(10, 0.10)(X ₃ , Y ₃)=(20, 0.05)(X ₄ , Y ₄)=(40, 0.05)Criteria curves and/or criteria data sets, including sets havingdifferent shapes or more complex shapes or both, can be determinedwithout undue experimentation. The intended use of the PCR applicationwill call for different approaches to establishing criteria lines. Theskilled artisan will readily appreciate that when high sensitivity isdesired in an assay, a low criteria line is used. For example, if anassay is designed for differentiating sequence variants, such aspopulation consensus sequence (i.e., a “wild type” sequence) versuspolymorphic or variant sequences (e.g., a “single nucleotidepolymorphism”), then a criteria line of higher value can be used,because the detection of limiting quantities of target nucleic acid isnot usually required in the determination of sequence variants.

The particular example shown in FIG. 11 does not exhibit positivebleedover from the internal control (IC) signal response to the assaysignal response. If positive IC signal response to assay bleedover wereto be present, a similar modification to the criteria could be made.Because the IC signal response should only occur over a narrow range ofFCN values, the criteria could be increased only in that limited range.

Generally, as further discussed herein, a FCN-MR response is determinedfor samples of known concentration across the target concentration rangeof interest to define the “normal” response. Additional studies in apopulation of samples that challenge the assay reaction may be run tosee how much deterioration in MR is acceptable before the assayperformance is compromised. These types of characterization analyses canbe used to establish criteria data or sets of criteria dataindependently of the standard deviation or other characteristics of thenoise or baseline observed when samples that do not contain targetnucleic acid are treated under amplification conditions.

According to other embodiments of the invention, criteria data also canbe determined in ways similar to determining a C_(t), for C_(t) analysisas has been done in the prior art. A particular assay under design canbe performed a number of times to characterize it's typical MR-FCNresponse. From this typical response, the criteria data set can bedefined. However, unlike C_(t) analysis, in FCN-MR, the response isindependent of intensity of signal and is easily reproducible, evenacross instruments of a particular type that produce highly variableresults with identical samples.

EXAMPLE 11 Alternative Region of Interest

It has been empirically found that the FCN value of an efficiencyrelated value as determined above can be advantageously adjusted toprovide an even more reproducible quantification value. For example,FIG. 12 is a plot of two sets of reaction data that illustrate howreaction curves for samples having the same initial concentration canvary due to different reaction anomalies. This figure illustrates tworesponses for samples containing equal quantities of an HIV targetnucleic acid. However, in one response, the signal obtained from thereaction falls off early due to an anomaly in the reaction. This falloff can cause a FCN value determined from the maximum of the shiftedratio curve to vary substantially between the two samples, asillustrated in FIG. 13. However, the figure also shows that the twogradient curves are more substantially similar at early time or cyclenumber, which is plotted on the x-axis of the graph.

Thus, the invention involves determining an offset from the cycle numberof maximum efficiency value (herein referred to as an FCN2 value), whichis the location of another point on a reaction curve that can be usedfor analysis as described herein. In further embodiments, an EfficiencyRelated Value Threshold (ERVT) or Ratio Threshold (RT) value can beselected and used to determine a cycle number region of interest. AnERVT or RT can be an automatically or empirically determined value for aparticular assay. The RT value can be set near to or at a criteria datalevel that is determined at the latter cycles during assay calibration.

One embodiment of a method of this invention starts at the FCN value onthe shifted ratio curve and determines an earlier reaction point wherethe curve crosses the RT value. This reaction point is reported as anFCN2 value. It is believed that the FCN2 value provides improvedlinearity in samples having low copy numbers, in contrast with FCNvalues for certain assays, such as reactions where non-specific productformation reduces the efficiency of product formation in samples havinglow copy numbers.

FIG. 13 illustrates the desirability of using an offset efficiencyvalue. This figure shows the shifted ratio curves for the responsesshown in FIG. 12 and an RT line at 0.03. For this example, the FCN andFCN2 values are shown in Table 1. TABLE 1 Response FCN FCN2 MR Well 4128.81 22.85 0.129 Well 42 28.06 22.92 0.097 Difference 0.75 0.07 0.032

In this example, the curve of one response flattens out early anddiffers in shape from the curve of the other response, and the shiftedratio curve shows a difference. The early flattening can cause theearlier peak. In this example, the FCN2 values are more closely matchedthan the FCN values. In general, FCN and FCN2 values have been found tobe more precise (lower standard deviations) than C_(t) values. Whilethese examples focus on use of the MR, it will be appreciated that othermeasures of the efficiency of the amplification reaction can be employedin the FCN and FCN2 embodiments of the present invention. Otherefficiency related transforms useful in the context of the presentinvention include, but are not limited to, (a) use of first derivative,(b) use of the differences between sequential periodic data points, and(c) use of the slope or gradient of the log of the growth curve.

EXAMPLE 12 Quantification Using MR-FCN Analysis

Quantification is often desired in various types of reaction analysis.In PCR reactions, for example, quantification generally refers to ananalysis of a reaction to estimate a starting amount or concentration ofa target having an unknown concentration. The invention involves methodsor systems or both for using an efficiency related value and a cyclenumber value (e.g., FCN) to perform a quantification. Specifically, theERV of a test sample is compared to one or more of the ERV of at leastone calibrator, preferably at least two calibrators, and, optionally, 3,4, 5, or 6 calibrators, each of which contains a known quantity of atarget nucleic acid.

In further embodiments, quantification can generally be understood asinvolving one or more calibration data captures and one or morequantification data captures. The calibration data and quantificationare related using a quantification relationship or equation.

In calibration, a relationship between captured data, or a value derivedfrom captured data (such as an FCN, FCN2, or MR, or combination of theforegoing), and one or more known starting concentration reactions isused to establish one or more parameters for a quantification equation.These parameters can then be used to determine the startingconcentrations of one or more unknown reactions.

Various methods and techniques are known in the art for performingquantification and/or calibration in reaction analysis. For example, indiagnostic PCR settings, it is not uncommon to analyze test samples in a96-well reaction plate. In each 96-well reaction plate, some wells arededicated to calibration reactions with samples having known initialconcentrations of target. The calibration values determined for thesesamples can then be used to quantify the samples of unknownconcentration in the well.

Two general types of calibration methods are referred to as one-pointcalibration and standard curve (e.g., multiple points) calibration.Examples of these types are set forth below. Any suitable calibrationmethod, however, can be used in the context of the present invention.

When there is no inhibition or interference, the PCR reaction proceedswith the target sequence showing exponential growth, so that after Ncycles of replication, the initial target concentration has beenamplified according to the relationship:Conc _(N) ∝Conc ₀(1+e)^(N)which can also be expressed as:${Conc}_{0} \propto {{Conc}_{N} \times \frac{1}{\left( {1 + e} \right)^{N}}}$where Conc_(N) represents the concentration of amplified target after Nreaction cycles, Conc₀ represents the initial target concentrationbefore amplification, N represents the cycle number and e represents theefficiency of the target amplification.Quantitative data analysis is used to analyze real time PCR reactioncurves so as to determine Conc₀ to an acceptable degree of accuracy.Previous C_(t) analysis methods attempt to determine a cycle number at areaction point where the Conc_(N) is the same for all reactions underanalysis. The FCN value determined by themethods of the invention provides a good estimate for the cycle number Nfor an assay in which no significant inhibition or signal degradationover the dynamic range of input target concentrations is demonstrated.The following proportionality relationship between a startingconcentration and FCN can be used:Conc ₀(FCN)∝1/(1+e)^(FCN)where Conc₀(FCN) represents the estimate of the initial targetconcentration determined by using the FCN value as determined by themethods of this invention.In other words, the lower the starting concentration of target, thehigher the FCN value determined for the PCR reaction. This relationshipcan be used for both calibration data and for quantification data.

This proportionality relationship can also be expressed as anequivalence, such asConc ₀(FCN)=K×1/(1+e)^(FCN)where K represents a calibration proportionality constant. Forcalibration data, Conc₀(FCN) represents a known concentration, such as500,000 copies of target nucleic acid/mL; the exponent FCN is a FCNcycle number determined as described above; and e represents theefficiency value for a reaction, with e=1 indicating a doubling eachcycle. These factors combine to form a relationship to allow fordetermination of the proportionality constant. Determination of theproportionality constant can only be made if there is a priori knowledgeof the efficiency, e, of the amplification reaction. This a prioriknowledge enables a one-point calibration. For quantification data, FCNvalues are determined for reactions involving samples having unknownconcentrations of target. The FCN values are then converted toconcentration values by use of the above equation. If the efficiency, e,is not known a priori, then a standard curve quantification method canbe used. In this case, for calibration data, different samples havingdifferent levels of known concentration are amplified, and the FCNvalues of the samples are determined. These FCN values can be plottedagainst the log (base 10) of the known concentrations to describe a log(concentration) vs. FCN response. For an assay that demonstrates nosignificant inhibition or signal degradation over the dynamic range ofinput target concentrations, this response is typically well-fitted by alinear curve. The following equation describes the form of this standardcurve:Log₁₀ (Conc ₀(FCN))=m×FCN+bwhere Log₁₀(Conc₀(FCN)) represents the log (base 10) of the initialtarget concentration, m represents the slope of the linear standardcurve, and b represents the intercept of the linear standard curve.By using two or more known concentration calibration samples, a linearregression can be applied to determine the slope, m, and intercept, b,of the standard curve. For quantification data, FCN values aredetermined for reactions involving test samples of unknownconcentration, which values are then converted to log (concentration)values by use of the above linear equation. Results can be reported ineither log (concentration) or concentration units by the appropriateconversion.

It should be noted that the one-point calibration equation is easilyconverted to this linear standard curve form:Conc ₀(FCN)=K×1/(1+e)^(FCN)Log₁₀ (Conc ₀(FCN))=−log₁₀ (1+e)×FCN+log₁₀ (K). The linear coefficient mcan be used to calculate the efficiency of the particular PCR reaction.

EXAMPLE 13 Quantification Adjustments

When PCR reactions are subjected to inhibition, the resulting real-timePCR signal intensity can be depressed or delayed. The effect of thissignal degradation on an efficiency related value such as MR is areduction in that value. In addition, the effect of signal degradationon the fractional cycle number is generally to identify the FCN at anearlier cycle number than would be expected for the uninhibitedreaction. These factors cause the plot of log (concentration) as afunction of FCN to be less well described by a linear curve fittingfunction. Although higher order curve fitting functions can be appliedfor a standard curve, a linear fit requires fewer calibration levels andis simpler to calculate.

Some of these problems can be addressed in a standard curve analysis byincorporating an ERV or Intensity value into the quantificationrelationships as discussed above. Thus, the equations above can berewritten a:Conc ₀(FCN _(Intensity Adj))∝Intensity/(1+e)^(FCN)Conc ₀(FCN _(MR Adj))∝MR/(1+e)^(FCN)where Intensity represents the response intensity (above background) atthe determined FCN value, MR represents the MR value as describedpreviously. Conc₀(FCN_(Intensity Adj)) represents the estimate of theinitial concentration of the target determined by using the FCN valueadjusted by using the Intensity value and Conc₀(FCN_(MR Adj)) representsthe estimate of the initial concentration of the target determined byusing the FCN value adjusted by using the MR value.

These expressions take advantage of the relationship observed betweenthe intensity at the selected FCN cycle or the MR determined at theselected FCN cycle, or both, and the change to the FCN value in thepresence of inhibition, as discussed above. The net effect is that theright hand side of the proportionality expressions above is relativelyinsensitive to inhibition and other factors that affect the PCRamplification curve, and, therefore, provide significant robustness asexpressions for determining the concentration values of the target.

The following discussion further explains the properties andrelationships of FCN, FCN_(Intensity Adj), and FCN_(MR Adj). Assumingthe efficiency is 1, the previous can be simplified to:Conc ₀(FCN)∝1/2^(FCN)Conc ₀(FCN _(Intensity Adj))∝Intensity/2^(FCN)Conc ₀(FCN _(MR Adj))∝MR/2^(FCN)Taking the Log base two of the expressions yields:Log₂(Conc ₀(FCN))∝FCNLog₂(Conc ₀(FCN _(Intensity Adj)))∝FCN−Log ₂(Intensity)Log₂(Conc ₀(FCN _(MR Adj)))∝FCN−Log ₂(MR)From the right sides of the expressions come the values for compensatingfor intensity or MR to adjust the FCN value by means of the followingformulas:FCN _(Int. Adj.) =FCN−Log₂(Intensity)FCN _(MR. Adj.) =FCN−Log₂(MR).This calculation then provides quantification by using adjusted FCNvalues analogous to using FCN values or C_(t) values. It should be notedthat the use of these adjusted FCN values provide significant robustnessto inhibition and other factors that affect PCR amplification, such asC_(t) values used in determining the concentrations of the target in theunknown samples. The plot of Log (concentration) vs. these adjusted FCNvalues is generally well fitted by a linear standard curve. Thus, thepresent invention provides a method for determining the quantity of atarget nucleic acid in a sample comprising involving the steps of (a)finding the period of time or cycle number of an amplification reactioncorresponding to a maximum of an efficiency related value, preferably ofan MR, and (b) adjusting that value by subtracting a logarithm of theIntensity or a logarithm of the MR, and (c) comparing the value obtainedto calibration data obtained using the same methodology.

EXAMPLE 14 Standard Curve Calibration

Development of a standard curve from known concentrations and usethereof for quantification is well known in the art and can be furtherunderstood from the following example. In a typical case, a number ofcalibration reactions (such as in wells in which the initialconcentrations are known) are used during each amplification or seriesof amplifications to perform the calibration operation. One problem thatarises with attempting to quantify a target nucleic acid in a samplethrough a large range of possible initial concentrations is thatquantification of lower quantities of target nucleic acid in anyparticular reaction becomes more difficult. For example, FIG. 14illustrates data for an assay designed to quantify the amount of HIV intest samples. The reactions were performed with eight replicates of sixknown concentrations of target nucleic acid, which were 50; 500; 5,000;50,000; 500,000; and 5,000,000 copies per mL. The assay data showsignificant signal suppression in reactions where the copy number is low(the curves farthest to the right). While quantity of the four highestconcentrations of target nucleic acid (the curve sets to the left)yielded precise results with low coefficients of variability, the twolowest concentrations produced less precise curves. The imprecisioncaused by the difficulties in quantifying low concentrations of targetnucleic acids in assays having a dynamic range of 100,000 to 1 or morecan be addressed by the following methods of this invention.

Because calibration runs in a reaction plate are relatively expensive,it is conventional to collect a minimal acceptable number of calibrationdata sets. For example, in one implementation, the average of tworeplicates each of the 500; 50,000; and 5,000,000 copy/mL samples arerun along with the diagnostic assays, thereby requiring perhaps sixwells in a 96 well plate to be used for calibration reactions.

Because the relationship between the cycle numbers and the log of thecalibrator concentration is substantially linear, a linear regressioncan be performed between a log (e.g., log₁₀) of the calibratorconcentrations and the cycle number. This regression can easily beperformed via the Excel program and other mathematical analysissoftware. FIG. 15 illustrates four linear standard curves generated fromthree-point calibration data using four different cycle number relatedvalues (e.g., FCN, FCN2, FCN_(MR Adj.), and FCN_(Int. Adj.)).

In each of the curve fit equations, the x-axis displays values of theLog₁₀ [Target] actual or known concentration. Thus, solving for xprovides an expression for converting from cycle number related valuesto Log₁₀ (Target) calculated concentration of the assay. If the assayresponse is not linear with Log (Target), a higher order or more complexregression, or a larger number of calibration reactions, or both, can beused. In this example, the following equations were determined:FCN=−3.0713*Log₁₀(Conc ₀)+31.295FCN 2=−3.0637*Log₁₀(Conc ₀)+25.006FCN _(MR adj)=−3.2344*Log₁₀(Conc ₀)+33.271FCN _(Int. adj)=−3.2870*Log₁₀(Conc ₀)+32.775

EXAMPLE 15 Comparing Quantification Using Different Cycle Number RelatedValues

In order to examine the different characteristics of calibrations usingthe different cycle number related values described above,quantification can be performed on various samples having knownconcentrations, and the concentrations calculated compared with theknown concentrations. In one example of such a comparison, the standardcurves having the parameters generated above were used to carry outquantification of the assay responses shown in FIG. 14. The mean of thecalculated concentrations of the eight replicates at each knownconcentration was compared to the known concentration value. FIG. 16compares log₁₀ of the known concentration values (x-axis) to the meansof the log₁₀ of each of the calculated concentrations for the eightsamples at each concentration.

As indicated by FIG. 16, the 50 copies/mL samples (log(concentration)=1.7) are slightly over-quantified (i.e., higher than theactual concentration) using FCN, while the accuracy for the FCN method(of the MR) at the higher concentrations is very good. FCN2 is moreaccurate at the lowest concentration, but somewhat under-quantified(i.e., lower than the actual concentration), and exhibit less linearityand accuracy at some higher concentrations. FCN_(MR Adj.) showed veryaccurate and linear quantification throughout the concentration range.FCN_(Int. Adj.) also showed substantial improvement in accuracy andlinearity compared to FCN, except for very slight under-quantificationat the lowest concentration. Accordingly, all four methods work well,but some are better than others for particular situations. Therefore,the skilled artisan can easily select an appropriate method for anyparticular application to obtain excellent results.

EXAMPLE 16 Quantification Using One-Point Calibration

A one-point calibration can be used for quantification. In this case,two wells at the 50,000 copies/mL concentration (Log (4.7)) were usedfor calibration. In order to calculate the calibration constant, thefollowing equation is used: K=Conc₀*2^(FCN), where K represents thecalibration constant, Conc₀represents the known concentration of thecalibrator, FCN represents the fractional cycle number of thecalibrator, and the efficiency of the reaction, e, as described earlier,is assumed to be 1. Similar calibration constants can be generated usingthe proportionality relationships such as FCN2, FCN_(MR Adj.) andFCN_(Int. Adj).

In this case, the constant was generated for two wells and the averagewas used. Once the calibration constant is generated, the concentrationfor each assay is calculated with the following equation:Conc=K_(FCN)/2^(FCN). FIG. 17 illustrates resulting from a one-pointcalibration.

As can be seen, the FCN results are elevated at the lowest twoconcentrations and accurate from log (Conc) equals 3.7 and above. FCN2shows improved accuracy at low concentrations compared to FCN, butunder-quantifies at log (Target) equal to 5.7 and 6.7. FCN-MR adjustedshows good linearity over the entire range with slightover-quantification at the two lowest concentrations. FCN-Intensityadjusted also shows good linearity with very slight under-quantificationat the lowest two concentrations. Accordingly, each of these embodimentsworks well and the skilled artisan can readily select from among theseoptions.

As discussed above, an FCN-MR analysis can be used to characterize aparticular reaction as positive or negative or to compare the reactionto criteria data, or both. These values can be used to quantify areaction. A variety of quantification methods can benefit from FCN-MRanalysis rather than C_(t) analysis.

In one embodiment, a FCN value, a FCN2 value, or a FCN adjusted valuecan be used in any way that a C_(t) value has been used in the priorart. Typically, but not necessarily, FCN-adjusted, FCN2-adjusted, orFCN-adjusted analysis can be applied to various sets of calibration datato thereby develop reference data curves or an equation for comparingthe result of a reaction in which the concentration of target is unknownto the results of reactions in which the concentration of target isknown. Thus, the present invention can be used to develop reference dataand to perform a comparison wherein two values (e.g., FCN-MR) are usedboth for developing reference data and also for making a comparison tothat data.

While experiments using the MR method regularly used differentpreprocessing steps on the captured data set before processing the dataset with a ratio function, most of these steps are not required. Inparticular, experimental results have indicated that scaling,normalization by a reference dye, baselining (both offset and slopecorrection), and filtering are not required. However, filtering hasgenerally been found to be desirable as it improves performance in thepresence of noise. Slope correction (for the baseline region) has alsobeen found to be desirable as it slightly improves discriminationbetween samples that do not contain target nucleic acid and those thatcontain very little target nucleic acid or suffer from significantinhibition of the amplification reaction. Generally, however, whenFCN_(Intensity adj) is used, it is preferable to use a normalizationtechnique, such as, but not limited to, scaling or normalization to areference dye.

EXAMPLE 17 MR Algorithm Applied to HBV Data Using a One-PointCalibration

HBV assays of control solutions ranging from 10 copies/reaction to 10⁹copies/reaction and negatives were processed on an ABI Prism 7000 withsix replicates at each concentration. The captured data was processedusing only a digital filter. FCN values were then calculated using a MRalgorithm as described above. The concentrations were calculated bymeans of a one-point calibration using the three of the responses at 10⁹copies/reaction as a reference calibrator.

Even without normalization, scaling, or baselining, the resultingquantification was very good, with the exception of an acceptable amountof over-quantification of the 10 copies/reaction and 100 copies/reactionsamples (i.e., the Log (Target)=1 and 2 samples). There was a very cleardistinction between the negatives and the 10 copies/reaction assays,with no false positives or false negatives. Additional results indicatedthat when the same data was quantified with C_(t) analysis, the 10copies/reaction and 100 copies/reaction assays are also slightlyover-quantified, and the precision at all concentrations above 10copies/reaction is better with the MR analysis. In this case, the C_(t)results were normalized, baselined, and calibrated by means of atwo-point calibration with three replicates each at concentrations 10³and 10⁷ copies/reaction.

FIG. 19 illustrates an example of the same HBV data using MR analysisand with FCN_(MR adj.), correction. Again, the quantification wasperformed by means of a one-point calibration with three responses atthe 10⁹ copies/reaction with no normalization, scaling, or baselining.As can be seen, the over-quantification of the low concentrations issignificantly reduced, i.e., the quantitative results are significantlyimproved.

EXAMPLE 18 MR Algorithm Applied to HIV Data

In this example, HIV assays of control solution were performed atconcentrations of negatives, 50 copies/mL, and 100 copies/mL, through10⁶ copies/mL in replicates of six. The responses were processed bymeans of the MR algorithm using FCN_(MR Adj.) with normalizing andbaselining. FIG. 21 illustrates results the example using MR analysisand two-point calibration, e.g., using two replicates of the 10² and 10⁵copies/mL responses as calibrators. There was clear differentiationbetween the negatives and the 50 copies/mL assays with no falsepositives or false negatives. As can be seen, there is good linearityand precision.

EXAMPLE 19 Validity Determination Using Target and IC (FCN, MR) Pairs

It has been found that pairs of reaction time or cycle number values andefficiency related values (e.g., pairs of FCN-MR values) can providevaluable information about a nucleic acid amplification reaction, e.g.,a PCR reaction, which can be further enhanced by considering data pairsfor both the internal control and target amplification reactions. Whilepairs for a target reaction alone carry important information aboutreaction efficiency and can be used for comparison with criteria data,additional factors that arise in processing samples or in the samplesthemselves may be better analyzed by considering control data as well.

For example, in processing specimens for use in PCR or other suitableamplification reactions, the sample can carry various inhibitors intothe reaction, which might be detectable through assessment of targetdata only. However, abnormal recovery of target nucleic acid duringsample preparation typically would not be detected by analysis of asingle amplification reaction. Furthermore, a target nucleic acid maypossess polymorphic sequences that could impair detection of the targetnucleic acid, e.g., if a probe is used that binds to a polymorphicregion of the sequence. Mismatches caused by the polymorphic sequence inthis region would affect the detected signal, and, consequently, theamplification might not appear as abnormal or inhibited using theevaluation of data pairs for a single amplification. Co-analysis of aninternal control together with analysis of the target amplificationresponses can provide accurate quantification of the target nucleic acidin such samples when other methods would typically indicate an invalidreaction.

Thus, pairs of reaction time or cycle number values and efficiencyrelated values can be used together to assess the validity of a givenreaction, such as in a given container or well. One could design theinternal control (IC) amplification reaction to be comparable inrobustness to the target amplification reaction, or slightly lessrobust. Robustness in this context means the sensitivity of the reactionperformance to factors that can affect the PCR processing pathway, suchas inhibition that results from sample preparation or the samplesthemselves, or to variability in transferring of the reaction mixture bypipette, such as transferring inaccurate amounts of amplificationreagents by pipette.

EXAMPLE 20 Multiple Criteria Data Curves

Multiple criteria curves for the pairs of cycle number value—efficiencyrelated value (e.g., FCN-MR pairs) can be developed and can havedifferent uses or levels of importance, particular for use with validitydetermination. For example, a first criteria curve can be selected so asto be able to discriminate reactive amplification signals fromnon-reactive responses. A second criteria curve can be selected so as tobe more constraining than the first type, so that it would be useful inidentifying sample responses that lead to accurate quantification incontrast to those having partial inhibition that might have lowerconfidence in quantification. FIG. 22 is a plot illustrating two typesof criteria data, wherein the lower horizontal line represents criteriadata suitable for differentiating negative from reactive reactions. Thesecond set of lines represents criteria data indicating the normal rangefor the FCN-MR pair responses. These criteria can be used to distinguishhigh confidence in quantification in contrast to a lower confidence thatmight be associated with a value outside this range due to partialreaction inhibition.

For example, the first type of criteria data that differentiatesreactive and non-reactive amplification reaction can be referred to as“MR criteria data.” These data act as a cutoff threshold—reactiveresponses will have MR values that exceed the MR criteria data, whereasnegative samples will have MR values that will not exceed the criteriavalue or criterion line. The criteria data is preferably set so thatnoise in the response signal does not exceed the criteria, nor will suchbiases as cross-talk or bleed-over.

The second type of criteria data is referred to as the MR normal range.This range would be the range of MR values for a given FCN over whichquantification of the sample is accurate. If a signal response issuppressed, the MR value observed will drop. As the MR value decreasesdue to inhibition, the FCN value can shift to earlier cycles, whereas athreshold based C_(t) might shift to later cycles. The MR normal rangewould be the range for MR values in a criteria data set for which achosen value related to a cycle number would provide an accuratequantitative result for the sample when used to determine theconcentration of target in the sample from the assay standard curve.

The “MR normal range” can be developed using a Bivariate Fit of the MRby FCN as will be understood in the art. FIG. 23, for example, shows aFCN-MR plot for HIV data from 50 copies/mL to 5,000,000 copies/mL. Thedata was analyzed by means of a statistics software package (such as JMP(SAS Institute, Inc.)) to apply a cubic curve fit to the data. Thiscubic curve fit is represented by the solid line in middle of thefigure. The upper and lower dashed curves represent the confidenceinterval generated using a confidence interval individual analysisoption with an alpha level of 0.001. TABLES 2A, 2B, and 2C illustratesample data input and output related to FIG. 23. TABLE 2A Summary of FitRSquare 0.971668 RSquare Adj 0.969737 Root Mean Square 0.023918 ErrorMean of Response 0.401317 Observations (or Sum 48 Wgts)Polynomial Fit Degree = 3MR = 0.6710196 − 0.0101107 FCN-0.0039387 (FCN-18.3056){circumflex over( )}2 − 0.0004202 (FCN-18.3056){circumflex over ( )}3

TABLE 2B Analysis of Variance Sum of Source DF Squares Mean Square FRatio Model  3 0.86331003 0.287770 503.0120 Error 44 0.02517212 0.000572Prob > F C. Total 47 0.88848215 <.0001

TABLE 2C Parameter Estimates Term Estimate Std Error t Ratio Prob > |t|Intercept 0.6710196 0.036617 18.33 <.0001 FCN −0.010111 0.002006 −5.04<.0001 (FCN-18.3056){circumflex over ( )}2 −0.003939 0.000198 −19.92<.0001 (FCN-18.3056){circumflex over ( )}3 −0.00042 0.000047 −8.93<.0001A statistically derived confidence interval, as shown, is a systematicapproach to determining which data points represent “normal” responsesand should therefore be quantified. Data points lying outside thisinterval are exceptional and are preferably identified to a humanoperator by a software program so that further investigation can bemade.

In alternative embodiments, such a curve can be simplified in the-formof one or more straight-line segments. This simplification can in somecases be performed by a technician viewing the raw data or may bederived from an alpha interval as discussed above.

A similar statistical fit can be performed on the internal control (IC)data. FIG. 24, for example, shows a plot of MR as a function of FCN forIC data, namely IC data associated with the data shown in FIG. 23. Thisdata can be used to determine an IC criteria, which, for example, can bea single value that is five standard deviations below the mean of the MRvalues of the IC or can be a range or box of values, for example, basedon the mean ±5 standard deviations of the MR and FCN values.

Thus, the present invention also provides a method for analyzing anamplification reaction, the method comprising establishing a “confidencecorridor”, which is a range of selected values provided in pairs inwhich the first value is a maximum efficiency related value (which ispreferably the MR), and the second value is a time value or cycle numbervalue at a reaction point (which optionally can be fractional). Themethod further comprises determining whether a maximum efficiency valueoccurring at any particular periodic time value or cycle number value ata reaction point (which optionally can be fractional) falls within theselected range. If the value does not, then further investigation, ordisregarding the results, is indicated. Any suitable method can be usedto establish the selected confidence corridor. Preferred methods includesetting the confidence corridor about 1, 2, 3, 5, 10, or any othersuitable number of standard deviations from the mean of data obtainedfrom a set of reactions used to characterize the assay. Another suitablemethod involves modifying the confidence corridor by observing knownaberrant or discrepant results and modifying the confidence corridor toexclude a portion of those aberrant or discrepant results in futureassays. The use of the confidence corridor of the present invention canbe applied to target nucleic acid quantification, analysis of any ofstandards, calibrators, controls, or to combinations of the foregoing.

EXAMPLE 21 Validity Analysis

FIG. 25 is a flow chart illustrating a logic analysis tree forassessment of assay validity through analysis of pairs of cycle number(e.g., FCN) minus of ERV (e.g., MR) for both the internal control andthe target amplification reactions. FIG. 26 is a flow chart illustratinga logic analysis tree for reporting target results with validitycriteria assessment using pairs of cycle number (e.g., FCN) minus ERV(e.g., MR). In the flow charts, FCN is used for clarity of illustration,but as noted elsewhere herein, other methods can be used to generate thereaction point value, for example, C_(t) method, FCN2, FCN_(MR Adj.) orFCN_(Int. Adj,.) or other suitable method.

Thus, a validity check can optionally proceed as a series of questionsregarding the internal control (IC) and/or target data.

In FIG. 25, the left-most arrow blocks provide general descriptions ofthe steps of the method. Details of method(s) can be understood furtherby considering the following. The method analyzes a cycle number/ERVpair from both a target and control (IC) reaction. Initially, if (1) theIC MR is above the IC MR criteria data, and then if (2) the IC FCN iswithin the normal range, and further if (3) the IC MR is within thenormal range, then reaction validity is confirmed.

As shown in the figure, an invalid result can be further characterizedor explained by considering one or more characteristics of the targetMR.

FIG. 26 illustrates a method for analyzing the target data for validreactions to further characterize a valid result as indicating (1) anon-reactive target sample, (2) a target at a concentration of less thanthe detecting limit of the assay, (3) a target present but with aquantification inhibited, possibly due to sub-type mismatch, or (4) avalid, quantifiable target reaction.

Thus, by combining the analysis based on multiple targets and using bothcycle number and efficiency related values, one can distinguish aninhibited sample from a sample that suffered from poor nucleic acidrecovery during sample preparation. The analysis makes use ofpre-established knowledge of the assay that is contained in the internalcontrol and target criteria data.

EXAMPLE 22 Validity Determination Using Peak Width

In contrast to the conventional C_(t) analyses in the prior art, whichonly presents a single value describing an amplification response, anefficiency related value analysis (and preferably an MR analysis) canprovide an efficiency related transform curve with data corresponding tothe time value or cycle number value of the entire amplificationreaction or any portion thereof. It has been discovered that within aspecific assay formulation, normal assay responses generate highlyreproducible efficiency related transform curves. One characteristic inparticular is the width of the peak of the efficiency related transformcurve. It has been found that the width of the peak of the efficiencyrelated transform, e.g., as defined by its width at the half maximumheight, varies very little even when the magnitude of the fluorescenceintensity varies greatly.

Any suitable method can be used to determine the width of the peak ofthe efficiency related value. FIG. 27 depicts one suitable method fordetermining the width of an efficiency related value peak. In FIG. 27,the full peak width is the width in cycles of the peak at it halfmaximum level. The HIV responses in FIG. 14 show normalized fluorescencefor samples of higher concentration at approximately 8, while thenormalized fluorescence for the samples of low concentration is as lowas about 1. Using the shifted ratio method to calculate an efficiencyrelated transform for each amplification reaction and computing the fullpeak width provides the results shown in FIG. 28. Even with aneight-fold change in final fluorescence intensity, the peak widths aresurprisingly conserved within a narrow range. Accordingly, the presentinvention provides amplification reaction validity criteria, wherein anamplification reaction is deemed valid when the width of the peak of anefficiency related value is contained within a selected rangecharacteristic of the amplification reaction. In FIG. 28, the dashedhorizontal lines in bold type represent the mean of the widthmeasurements plus and minus 10 standard deviations. Width measurementsthat are not within the range of about 5.5 and 8.0 (as shown in FIG. 28)are considered invalid or at least suspect. The skilled artisan canreadily vary the parameters describing the acceptance interval,depending on the requirements of the particular assay and without undueexperimentation.

Peak width can be used to detect an abnormal assay response. The fullpeak width calculation was applied to the assay data that contained theabnormal response shown in FIG. 12. The results are presented in FIG.29. As can be seen, normal responses for this data set produce full peakwidths between about 6 and 9 cycles whereas full peak width of well 42is 17.42. Accordingly, the amplification reaction of well 42 is abnormaland is disregarded.

The full peak width calculation will be affected by abnormal variationsin amplification response that occur both before and after the reactionpoint value (e.g., the FCN) of the efficiency related value. Abnormalvariations that occur after the reaction point value of the efficiencyrelated value are not considered for an assay validity test, becausethey cannot affect assay quantification by the MR method. This optioncan readily be achieved using the half peak width calculationillustrated in FIG. 27 or its equivalent. In the illustrated example,only the width in periodic time units from about the half-maximumefficiency related transform up to about the reaction point value of themaximum efficiency related value is used. Of course, other suitablemethods for measuring peak widths and half-peak widths are known in theart.

EXAMPLE 23 Software Embodiments

The systems of this invention can be incorporated into a multiplicity ofsuitable computer products or information instruments. Some details of aMR software implementation are provided below. Specific user interfacedescriptions and illustrations are taken to illustrate specificembodiments only and any number of different user interface methodsknown in the information processing art can be used in systems embodyingthis invention. The invention can also be used in systems wherevirtually all of the options described below are preset, calculated, orprovided by an information system, and, consequently, provide little orno user interface options. In some cases, details and/or options of aprototype system are described for exemplification purposes; many ofthese options and/or details may not be relevant or available for aproduction system.

Furthermore, software embodiments can include various functionalities,such as, for example, processing reactions with one or two targetreactions, or one or more internal control reactions, or reference data,or combinations of the foregoing. A software system suitable for use inthis invention can provide any number of standard file handlingfunctions such as open, close, printing, saving, etc.

FIG. 30 illustrates a user interface for processing PCR data accordingto this invention. In this interface, the selection of appropriatedye(s) corresponding to the target assay, internal control, andreference responses are selected from popup lists in the upper leftportion of the window. Tabs for selecting different viewing options arepositioned in the middle of the window and are arranged horizontally.FIG. 30 shows that the tab displaying the MR-FCN plot has been selected.FIG. 31 illustrates a user interface showing the same data for well 1,but displaying the shifted ratio curve. Other tabs allow viewing of theraw fluorescence data, normalized fluorescence, and baselined data forall the responses. In addition, a tab allows inspection of each responseindividually. Fields to the right of the plot show calculated responsevalues such as MR, FCN, C_(t.) and standard deviation in the baselineregion. Below these calculated values are radio buttons allowing theuser to display either the assay data or the internal control data.

Embodiment in a Programmed Information Appliance

FIG. 32 is a block diagram showing an example of a logic device in whichvarious aspects of the present invention may be embodied. As will beunderstood from the teachings provided herein, the invention can beimplemented in hardware or software or both. In some embodiments,different aspects of the invention can be implemented in eitherclient-side logic or server-side logic. Moreover, the invention orcomponents thereof can be embodied in a fixed media program componentcontaining logic instructions or data, or both, that when loaded into anappropriately configured computing device can cause that device toperform according to the invention. A fixed media component containinglogic instructions can be delivered to a viewer on a fixed medium forphysically loading into a viewer's computer or a fixed medium containinglogic instructions can reside on a remote server that a viewer canaccess through a communication medium in order to download a programcomponent.

FIG. 32 shows an information instrument or digital device 700 that canbe used as a logical apparatus for performing logical operationsregarding image display or analysis, or both, as described herein. Sucha device can be embodied as a general-purpose computer system orworkstation running logical instructions to perform according to variousembodiments of the present invention. Such a device can also becustomized and/or specialized laboratory or scientific hardware thatintegrates logic processing into a machine for performing various samplehandling operations. In general, the logic processing components of adevice according to the present invention are able to read instructionsfrom media 717 or network port 719, or both. The central processing unitcan optionally be connected to server 720 having fixed media 722.Apparatus 700 can thereafter use those instructions to direct actions orperform analysis as described herein. One type of logical apparatus thatcan embody the invention is a computer system as illustrated in 700,containing CPU 707, optional input devices 709 and 711, storage media715, e.g., disk drives, and optional monitor 705. Fixed media 717, orfixed media 722 over port 719, can be used to program such a system andcan represent disk-type optical or magnetic media, magnetic tape, solidstate dynamic or static memory, etc. The invention can also be embodiedin whole or in part as software recorded on this fixed media.Communication port 719 can also be used to initially receiveinstructions that are used to program such a system and represents anytype of communication connection.

FIG. 32 shows additional components that can be part of a diagnosticsystem. These components include a viewer or detector 750 or microscope,sample handler 755, UV or other light source 760 and filters 765, and aCCD camera or capture device 780 for capturing signal data. Theseadditional components can be components of a single system that includeslogic analysis and/or control. These devices may also be essentiallystand-alone devices that are in digital communication with aninformation instrument such as 700 via a network, bus, wirelesscommunication, etc., as will be understood in the art. Components ofsuch a system can have any convenient physical configuration and/orappearance and can be combined into a single integrated system. Thus,the individual components shown in FIG. 42 represent just one examplesystem.

The invention can also be embodied in whole or in part within thecircuitry of an application specific integrated circuit (ASIC) or aprogrammable logic device (PLD). In such a case, the invention can beembodied in a computer understandable descriptor language, which may beused to create an ASIC, or PLD, that operates as described herein.

Other Embodiments

The invention has now been described with reference to specificembodiments. Other embodiments will be apparent to those of skill in theart. In particular, a viewer digital information appliance has generallybeen illustrated as a computer workstation such as a personal computer.However, the digital computing device is meant to be any informationappliance suitable for performing the logic methods of the invention,and could include such devices as a digitally enabled laboratory systemsor equipment, digitally enabled television, cell phone, personal digitalassistant, etc. Modification within the spirit of the invention will beapparent to those skilled in the art. In addition, various differentactions can be used to effect interactions with a system according tospecific embodiments of the present invention. For example, a voicecommand may be spoken by an operator, a key may be depressed by anoperator, a button on a client-side scientific device may be depressedby an operator, or selection using any pointing device may be effectedby the user.

It is understood that the examples and embodiments described herein arefor illustrative purposes and that various modifications or changes inlight thereof will be suggested by the teachings herein to personsskilled in the art and are to be included within the spirit and purviewof this application and scope of the claims.

All publications, patents, and patent applications cited herein or filedwith this application, including any references filed as part of anInformation Disclosure Statement, are incorporated by reference in theirentirety.

1. A method of determining whether a test sample contains a targetnucleic acid, the method comprising: (a) contacting the test sample withat least one amplification agent; (b) amplifying at least a portion ofthe target nucleic acid in the sample; (c) measuring signals obtained atvarious points in the amplification, the signals being proportional tothe amount of the target nucleic acid present; (d) determining anefficiency related transform of the amplification reaction; (e)determining an efficiency related value that is the maximum magnitude ofthe efficiency related transform; and (f) determining that the testsample contains a target nucleic acid if the efficiency related valuefor the amplification exceeds a selected value.
 2. The method of claim1, wherein the efficiency related transform of the amplificationreaction is selected from the group consisting of (1) ratio transform ofthe signals obtained from the amplification, (2) the derivative of thelog of the signals obtained from the amplification, and (3) the firstderivative of the signals obtained from the amplification.
 3. The methodof claim 2, wherein the efficiency related transform is the firstderivative of the signals obtained from the amplification, wherein thefirst derivative of the signals obtained from the amplification reactionis equal to the difference between two consecutive signals obtained fromthe amplification reaction divided by the magnitude of the intervalbetween the consecutive signals.
 4. The method of claim 2, wherein theefficiency related transform is the first derivative of the signalsobtained from the amplification, wherein the first derivative of thesignals obtained from the amplification reaction is calculated bymathematical manipulation of a curve fitted to the signals obtained fromthe amplification reaction.
 5. The method of claim 1, wherein the stepof determining whether the efficiency related value exceeds a selectedvalue is performed by comparing the efficiency related value to acriterion curve, wherein the criterion curve is determined by: (a)performing a plurality of amplification reactions on negative samples,said negative samples being samples that lack the target nucleic acid;(b) determining the efficiency related value for each negative sample;(c) determining the mean and the standard deviation of the efficiencyrelated values of the negative samples; and (d) determining that anysample having any efficiency related value exceeding the mean by aselected multiple of the standard deviation of the efficiency relatedvalues of the negative samples.
 6. The method of claim 5, wherein anysample having any efficiency related value exceeding the mean by fromone to about 20 times the standard deviation of the efficiency relatedtransform of the negative samples is deemed to contain a target nucleicacid.
 7. The method of claim 1, wherein the selected value of step (e)varies according to the particular reaction point at which theefficiency related value occurs.
 8. The method of claim 1, wherein theselected value of step (e) is determined by (1) amplifying a pluralityof samples to determine the efficiency related values and (2) selectinga value that is higher than all of the efficiency related values for thenegative samples.
 9. The method of claim 1, wherein the selected valueis determined by (1) amplifying a plurality of samples to determine theefficiency related values and (2) selecting a value that separates theefficiency related values of the negative samples from the efficiencyrelated values of the positive samples.
 10. The method of claim 1,wherein the efficiency related value is the maximum gradient of the logof the amplification response.
 11. The method of claim 1, wherein theefficiency related value is the maximum ratio of the amplificationresponse.
 12. The method of claim 1, wherein the efficiency relatedvalue is the maximum first derivative of the amplification response. 13.A method for quantifying the concentration of a target nucleic acid in asample, comprising the steps of: (a) contacting the nucleic acid samplewith at least one amplification agent; (b) amplifying at least a portionof the target nucleic acid in the sample; (c) measuring signals obtainedat various points in the amplification, the signals being proportionalto the amount of the target nucleic acid present; (d) applying a ratiotransform to the signals measured in step (c); (e) identifying areaction point in the amplification reaction corresponding to themaximum value of the ratios obtained in steps (c) and (d); and (f)calculating from the reaction point identified in step (e) theconcentration of target nucleic acid in the sample.
 14. The method ofclaim 13, wherein the first signal is obtained at a reaction point thatis subsequent to the reaction point at which the second signal isobtained, wherein the identified reaction point corresponds to themaximum value of the ratio obtained in step (e).
 15. The method of claim14, wherein the points represent cycles of amplification, wherein theperiod of time between signals obtained is equal to the period of timerequired to complete each amplification cycle, wherein there is onefirst signal and one second signal.
 16. The method of claim 14, whereinthe points represent points of time in the amplification, wherein theperiod of time between signals obtained is equal to the period of timerequired to complete each amplification cycle, wherein there is onefirst signal and one second signal.
 17. The method of claim 13, furthercomprising the step of removing the slope determined from a baselinesignal from the signals measured in step (c) before executing step (d).18. The method of claim 13, wherein additional signal values aregenerated by interpolating between points where the signals are measuredin step (c).
 19. The method of 13, wherein step (d) further comprisesthe step of subtracting a constant from each ratio obtained.
 20. Themethod of claim 19, wherein the constant is about 1, whereby a shiftedratio is obtained.
 21. A method for quantifying the concentration of atarget nucleic acid in a sample, said method comprising the steps of:(a) contacting the test sample with at least one amplification agent;(b) amplifying at least a portion of the target nucleic acid in thesample; (c) measuring signals obtained at various points in theamplification, the signals being proportional to the amount of thetarget nucleic acid present; (d) determining an efficiency relatedtransform of the amplification reaction; (e) determining an efficiencyrelated value that is the maximum magnitude of the efficiency relatedtransform; (e) identifying a reaction point in the amplificationreaction corresponding to the maximum magnitude of the efficiencyrelated value obtained in step (e); and (f) calculating an adjustedreaction point.
 22. The method of claim 21, wherein the adjustedreaction point is equal to the reaction point minus the log base 2 ofthe efficiency related value.
 23. The method of claim 21, wherein theadjusted reaction point is equal to the reaction point minus the logbase 2 of the signal intensity above background.
 24. The method of claim21 wherein the efficiency related value is derived from the shiftedratio of the amplification response.
 25. The method of claim 21, whereinthe efficiency related value is the maximum ratio of the amplificationresponse.
 26. The method of claim 1, wherein the efficiency relatedvalue is the maximum gradient of the log of the amplification response.27. The method of claim 1, wherein the efficiency related value is themaximum first derivative of the amplification response.
 28. A method foranalyzing a nucleic acid amplification reaction, the method comprisingthe steps of: (a) contacting a nucleic acid sample with at least oneamplification agent; (b) amplifying at least a portion of the targetnucleic acid in the sample; (c) measuring signals obtained at variouspoints in the amplification, the signal being proportional to the amountof the target nucleic acid present; (d) determining an efficiencyrelated transform of the amplification reaction; (e) determining anefficiency related value that is the maximum magnitude of the efficiencyrelated transform; (f) establishing a range for pairs of data comprisingan efficiency related value and a reaction point value; (g) determiningwhether an efficiency related value occurring at any particular reactionpoint value falls within the range established in step (f); and (h) ifthe efficiency related value is not within the range of valuesestablished for the efficiency related value corresponding to aparticular reaction point value, then the reaction is deemed potentiallysubject to error.
 29. The method of claim 28, wherein the efficiencyrelated value is the maximum gradient of the log of the amplificationresponse.
 30. The method of claim 28, wherein the efficiency relatedvalue is the maximum ratio of the amplification response.
 31. The methodof claim 28, wherein the efficiency related value is the maximum firstderivative of the amplification response.
 32. The method of claim 28,wherein the reaction point value is a cycle number.
 33. The method ofclaim 32, wherein the cycle number is a fractional cycle number.
 34. Themethod of claim 28, wherein the nucleic acid amplification reaction isdesigned to detect the presence of a target nucleic acid in the nucleicacid sample.
 35. The method of claim 28, wherein the nucleic acidamplification reaction amplifies a standard, calibrator, or controlnucleic acid.
 36. The method of claim 25, wherein a series of samplesare amplified to provide an assay characterization data set, wherein foreach sample a maximum efficiency related value and reaction point valueare established, and wherein a range of reliable efficiency relatedvalues for each reaction point value is established.
 37. The method ofclaim 36, wherein the range of reliable efficiency related values is aselected number of standard deviations greater than and less than themean maximum efficiency related value for each reaction point valuerepresented in the characterization data set.
 38. The method of claim25, further comprising the steps of: observing a discrepant result froman assay for detecting a target nucleic acid in which the efficiencyrelated value is within the selected range and the sample did notcomprise a target nucleic acid, and modifying the selected range ofacceptable efficiency related transforms at a particular reaction pointvalue so as to exclude the efficiency related value of the reactionproducing the discrepant result.
 39. A method of analyzing a nucleicacid amplification reaction, the method comprising the steps of: (a)contacting a sample comprising a nucleic acid with at least oneamplification agent; (b) amplifying at least a portion of the nucleicacid in the sample; (c) periodically measuring a signal that isproportional to the amount of the target nucleic acid present; (d)determining an efficiency related transform of the amplificationreaction obtained from the data collected in step (c) at pointsthroughout the amplification reaction; (e) identifying a peak in theefficiency related transform as a function of time or cycle number; (g)determining the width of the peak; (h) comparing the width of the peakto a selected range of acceptable peak widths; and (i) declaring thenucleic acid amplification reaction abnormal if the peak widthdetermined is greater than or less than the selected range of acceptablepeak widths.
 40. The method of claim 39, wherein the peak width iscalculated using only efficiency related transforms that occur at orbefore the reaction point value of the efficiency related value.
 41. Themethod of claim 39, wherein the efficiency related transform is theshifted ratio.
 42. The method of claim 39, wherein the efficiencyrelated value is the maximum gradient of the log of the amplificationresponse.
 43. The method of claim 39, wherein the efficiency relatedvalue is the maximum ratio of the amplification response.
 44. The methodof claim 39, wherein the efficiency related value is the maximum firstderivative of the amplification response.
 46. The method of claim 39,wherein the points in the amplification reaction are measured infractional cycle numbers.
 47. A method for quantifying the concentrationof a target nucleic acid in a sample, comprising the steps of: (a)contacting the nucleic acid sample with at least one amplificationreagent; (b) amplifying at least a portion of the target nucleic acid inthe sample; (c) periodically measuring signals that are proportional tothe amount of the target nucleic acid present; (d) determining anefficiency related transform from the signals measured in step (c) forthe amplification reaction, wherein the efficiency related transform isselected from the group consisting of the ratio transform of the signalof step (c), the shifted ratio transform of the signal of step (c), thefirst derivative of the signal of step (c), the differences betweensequential signals obtained in step (c), and the slope or gradient ofthe log of the signals obtained in step (c), wherein the efficiencyrelated transform comprises at least two identifiable data subsets, afirst data subset forming a baseline portion in which the efficiencyrelated transform is essentially constant; and a second data subsetforming a growth region in which the efficiency related transformapproaches or reaches a maximum value, (e) fitting a line or finding anaverage value for the baseline region of the efficiency relatedtransform of step (d); (f) selecting a threshold line that is parallelto and has a greater value than the line of step (e) or selecting athreshold value that has a greater value than the average value of step(e); (g) determining the reaction point value at which the efficiencyrelated transform of step (d) exceeds the threshold line or thresholdvalue of step (f); and (h) using the result of step (g) to determine thequantity of target nucleic acid in the sample.
 48. The method of 47,wherein additional signal values are generated by interpolating pointsbetween the signals measured in step (c).
 49. A method for quantifyingthe concentration of a target nucleic acid in a sample, the methodcomprising the steps of: (a) contacting the nucleic acid sample with atleast one amplification agent; (b) amplifying at least a portion of thetarget nucleic acid in the sample; (c) periodically measuring signalsthat are proportional to the amount of the target nucleic acid present;(d) determining an efficiency related transform from the signalsmeasured in step (c) for the amplification reaction; wherein theefficiency related transform is selected from the group consisting ofthe ratio transform of the signal measured in step (c) and the shiftedratio transform of the signal measured in step (c), wherein theefficiency related transform comprises at least two identifiable datasubsets, a first data subset forming a baseline portion in which theefficiency related transform is essentially constant; and a second datasubset forming a growth region in which the efficiency related transformapproaches or reaches a maximum value, (e) fitting a line or finding anaverage value for the baseline region of the ratios of step (d); (f)selecting a threshold line that is parallel to and has a greater valuethan the line of step (e) or selecting a threshold value that has agreater value than the average value of step (e); (g) determining thereaction point value at which the efficiency related transform of step(d) exceeds the threshold line or threshold value of step (f); and (h)using the result of step (g) to determine the quantity of target nucleicacid in the sample.
 50. The method of 49, wherein additional signalvalues are generated by interpolating points between the signalsmeasured in step (c).
 51. A method of quantifying a target nucleic acidin a sample, the method comprising the steps of: (a) contacting thesample with amplification or detection reagents such that the targetnucleic acid is amplified; (b) measuring and recording a signalproportional to the amount of the nucleic acid or to the amplifiedamount of nucleic acid in the sample at time-based or cycle-basedintervals; (c) determining a time or cycle of the Maximum Ratio at whichthe ratio of the signal at time or cycle n+1 to the signal at time orcycle n is greatest; and (d) determining the quantity of the targetnucleic acid in the sample.
 52. The method of claim 51, wherein themagnitude of the maximum ratio is compared to criteria to determine thequantity of the target nucleic acid in the sample in the amplificationreaction.
 53. The method of claim 51, wherein the amplification reagentsare capable of causing a PCR reaction to occur in the presence of thetarget nucleic acid.
 54. A method of quantifying a target nucleic acidin a sample, the method comprising the steps of: (a) contacting thesample with amplification or detection reagents such that the targetnucleic acid is amplified; (b) measuring and recording a signalproportional to the amount of the nucleic acid or to the amplifiedamount of nucleic acid in the sample at time-based or cycle-basedintervals; (c) determining a region in the data in which the average of(a) the ratio of the signal at time or cycle n+1 to the signal at timeor cycle n and (b) the ratio of the signal at time or cycle n to thesignal at time or cycle n−1 is greatest; and (d) determining thequantity of the target nucleic acid in the sample.
 55. The method ofclaim 54, wherein the magnitude of the maximum ratio is compared tocriteria to determine the quantity of the target nucleic acid in thesample in the amplification reaction
 56. The method of claim 54, whereinthe amplification reagents are capable of causing a PCR reaction tooccur in the presence of the target nucleic acid.
 57. The method ofclaim 1, wherein the efficiency related value is the maximum shiftedratio transform of the amplification response.
 58. The method of claim28, wherein the efficiency related value is the maximum shifted ratiotransform of the amplification response.